Question Set A

CBSE 12th Physics Alternating Current Important Questions And Answers Study Material - QB365

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Questions:

Multiple Choice Question

64 x 1 = 64

A voltage signal is described by \(V =V_0 \text { for } 0 \leq t \leq \frac{T}{2} =0 \text { for } \frac{T}{2} \leq t \leq T\) for a cycle. Its rms value is

(a)

\(\frac{V_0}{\sqrt{2}}\)

(b)

\(V_0\)

(c)

\(\frac{V_0}{2}\)

(d)

\(\sqrt{2} V_0\)

When an alternating voltage E - E₀, sinot is applied to a circuit, a current \(I=I_0 \sin \left(\omega t+\frac{\pi}{2}\right)\), sincov flows through it. The average power dissipated in the circuit is

(a)

\(E_{\mathrm{rms}} \cdot I_{\mathrm{rms}}\)

(b)

\(E_0 I_0\)

(c)

\(\frac{E_0 I_0}{\sqrt{2}}\)

(d)

zero

A circuit is connected to an AC source of variable frequency. As, the frequency of the source isincreased, the current first increases and then decreases. Which of the following combination of elements is likely to comprise the circuit?

(a)

L, C and R

(b)

L and C

(c)

L and R

(d)

R and C

The impedance of a series L-C-R circuit is

(a)

\(R+X_L+X_C\)

(b)

\(\sqrt{\frac{1}{X_C^2}+\frac{1}{X_L^2}+R^2}\)

(c)

\(\sqrt{X_L^2-X_C^2+R^2}\)

(d)

\(\sqrt{R^2+\left(X_L-X_C\right)^2}\)

If the reading of the voltmeter V₁ is 40 V, then the reading of voltmeter V₂ is

(a)

30 V

(b)

58 V

(c)

29 V

(d)

15 V

An iron cored coil is connected in series with an electric bulb with an AC source as shown in figure. When iron piece is taken out of the coil, the brightness of the bulb will

(a)

decrease

(b)

increase

(c)

remain unaffected

(d)

fluctuate

A 300Ω resistor and a capacitor of (25/π) µF are connected in series to a 200 V-50 Hz AC source. The current in the circuit is

(a)

0.1 A

(b)

0.4 A

(c)

0.6 A

(d)

0.8 A

A 15Ω resistor, an 80 mH inductor and a capacitor of capacitance Care connected in series with a 50 Hz AC source. If the source voltage and current in the circuit are in phase, then the value of capacitance is

(a)

100 µF

(b)

127 µF

(c)

142 µF

(d)

160 µF

The voltage across a resistor, an inductor and a capacitor connected in series to an AC source are 20 V, 15 V and 30 V, respectively. The resultant voltage in the circuit is

(a)

(b)

20 V

(c)

25 V

(d)

65 V

10.

In a circuit, the phase difference between the alternating current and the source voltage is π/ 2 Which of the following cannot be the element(s) of the circuit?

(a)

Only C

(b)

Only L

(c)

L and R

(d)

L or C

11.

The rms current in a circuit connected to a 50 Hz AC source is 15 A. The value of the current 1/600 s after its value becomes zero is

(a)

\(\frac{15}{\sqrt 2} A\)

(b)

\({15}{\sqrt 2} A\)

(c)

\(\frac{\sqrt 2}{15} A\)

(d)

\(8 A\)

12.

The rms value of a current given by \(i=\left(i_1 \cos \omega t+i_2 \sin \omega t\right)\) is

(a)

\(\frac{1}{\sqrt{2}}\left(i_1+i_2\right)\)

(b)

\(\frac{1}{\sqrt{2}}\left(i_1-i_2\right)\)

(c)

\(\frac{1}{\sqrt{2}} \sqrt{\left(i_1^2+i_2^2\right)}\)

(d)

\(\frac{1}{\sqrt{2}}\left(i_1^2+i_2^2\right)\)

13.

An AC source V = 282 sin (100 t) volt is connected across a 1 \(\mu\)F capacitor. The rms value of current in the circuit will be (take, \(\sqrt{2}\) =1.41)

(a)

10 mA

(b)

20 mA

(c)

40 mA

(d)

80 mA

14.

A conductor of 10\(\Omega \) is connected across 6V ideal source. The power supplied by the sources to the conductor is

(a)

1.8 W

(b)

2.4 W

(c)

3.6 W

(d)

7.2 W

15.

Which of the following statements about a series LCR circuit connected to an AC source is correct?

(a)

If the frequency of the source is incresed, the impedance of the circuit first decreases and then increases.

(b)

If the net reactance (X_t= X_C) of circuit becomes equal to its resistance, then the current leads the voltage \(45^{\circ}\)

(c)

At resonance more the voltage drop across the inductor is than that across the capacitor.

(d)

At resonance, the voltage drop across the capacitor is more than that across the inductor.

16.

An AC voltage V = V_osin\(\omega\)t is applicd to a series combination of a resistor R and an element X. The instantancous current in the circuit is \(I=I_0 \sin \left(\omega t+\frac{\pi}{4}\right)\) . Then, which of the following is correct?

(a)

X is a capacitor and X _C = \(\sqrt2\)R

(b)

X is a inductor and X _L= R

(c)

X is a inductor and X _L=\(\sqrt2\) R

(d)

X is a capacitor X _C = R

17.

Figure shows the variation of inductive reactance X_L,of two ideal inductors of inductances L₁ and L₂, with angular frequency \(\omega\) The value of \(\frac{L_1}{L_2}\)is

(a)

\(\sqrt{3}\)

(b)

\(\frac{1}{\sqrt{3}}\)

(c)

(d)

\(\frac{1}{3}\)

18.

Reciprocal of impedance is

(a)

susceptance

(b)

conductance

(c)

admittance

(d)

transconductance

19.

The reactance of a capacitor C is X. If both the frequency and capacitance be doubled, then new reactance will be

(a)

(b)

(c)

(d)

\(\frac{X}{4}\)

20.

A coil of self-inductance L is connected in series with a bulb B and an ac source. Brightness of the bulb decreases when

(a)

frequency of the ac source is decreased.

(b)

number of turns in the coil is reduced

(c)

a capacitance of reactance X_C = X_L in included

(d)

an iron rod is inserted in the coil

21.

What is the value of inductance L for which the current is maximum in a series LCR-circuit with C = 10 μF and ω = 1000 S^-1?

(a)

100 mH

(b)

1 mH

(c)

10 mH

(d)

cannot be calculated unless R is known

22.

A transformer is used to light a 100 W and 110 V lamp from a 220 V mains. If the main current is 0.5A, the efficiency of the transformer is approximately

(a)

30%

(b)

50%

(c)

90%

(d)

10%

23.

In a series, LCR-circuit, resonant frequency depends on

(a)

\(\frac{L}{C} \)

(b)

\(\sqrt{L C} \)

(c)

\(\frac{1}{\sqrt{L C}} \)

(d)

\(\sqrt{\frac{L}{C}}\)

24.

In an a.c. generator, a coil with N turns, all of the same area A and total resistance R, rotates with frequency ω in a magnetic field B the maximum value of emf generated in the coil is

(a)

NABR

(b)

NABω

(c)

NABRω

(d)

NAB

25.

The core of any transformer is laminated so as to

(a)

reduce the energy loss due to eddy currents

(b)

make it light weight

(c)

make it robust and strong

(d)

increase the secondary voltage

26.

In an ac circuit the voltage applied is ε = ε₀sin wt. The resulting current in the circuit is I = I₀ sin (ωt - π/2). The power consumption in the circuit is given by

(a)

\( P=\sqrt{2} \varepsilon_{0} I_{0} \)

(b)

\( P=\frac{\varepsilon_{0} I_{0}}{\sqrt{2}}\)

(c)

\(\boldsymbol{P}=\mathbf{0} \)

(d)

\( P=\frac{\varepsilon_{0} I_{0}}{2} \)

27.

An ac circuit has a resistance of 12 ohm and an impedance of 15 ohm. The power factor of the circuit will be

(a)

0.8

(b)

0.4

(c)

0.125

(d)

1.25

28.

In an LCR-series ac circuit, the voltage across each of the component L, C and R is 50 V. The voltage across the LC-combination will be

(a)

50 V

(b)

\(50 \sqrt{2} \mathrm{~V}\)

(c)

100 V

(d)

zero

29.

The phase difference between the alternating current and emf is π/2. Which of the following cannot be the constituent of the circuit?

(a)

C alone

(b)

L alone

(c)

L and C

(d)

R and L

30.

As the frequency of an ac circuit increases, the current first increases and then decreases. What combination of circuit elements is most likely to comprise the circuit?

(a)

Inductor and capacitor.

(b)

Resistor and inductor

(c)

Resistor and capacitor.

(d)

Inductor only.

31.

The phenomenon of resonance is common among systems that have a tendency

(a)

to oscillate at a' particular frequency

(b)

to get maximum amplitude

(c)

Both (a) and (b)

(d)

Neither (a) nor (b)

32.

In R-L-C series circuit with C = 1.00 nF two values of R are
(i) R = 100 \(\Omega\)and
(ii) R = 200 \(\Omega\) For the source applied with V_m = 100 V. Resonant frequency is

(a)

1 x 10³rad/s

(b)

1 x 10⁶rad/s

(c)

1.56 x 10⁶rad/s

(d)

1.75 x 10³rad/s

33.

The value of power factor is maximum in an alternating circuit, when circuit consists

(a)

only inductive

(b)

only capacitive

(c)

only L- C

(d)

only resistive

34.

In an AC circuit, the instantaneous values of emf and current are e = 200 sin (314) t V and I = sin (314t + \(\pi /3\)) A. The average power consumed is

(a)

200 W

(b)

100 W

(c)

50 W

(d)

25 W

35.

A 60 W load is connected to the secondary of a transformer whose primary draws line voltage of 220 V. If a current of 0.54 A flows in the load, then what is the current in the primary coil?

(a)

2.7 A

(b)

0.27 A

(c)

1.65 A

(d)

2.85 A

36.

In a series L-C-R circuit, the capacitance Cis changed to 4C. To keep the resonant frequency same, the inductance must be changed by

(a)

(b)

L/2

(c)

(d)

L/4

37.

A 15.0 \(\mu\)F capacitor is connected to a 220 V,50 Hz source. The capacitive reactance is

(a)

220 \(\Omega\)

(b)

215 \(\Omega\)

(c)

212 \(\Omega\)

(d)

204 \(\Omega\)

38.

The amplitude of the oscillating current in the a pure capacitive AC circuit is, if V = V_m capacitance = C.

(a)

\(\omega\)CV_m

(b)

2\(\omega\)CV_m

(c)

\(\frac{\omega C V_{m}}{4}\)

(d)

\(\frac{3 \omega C V_{m}}{2}\)

39.

Current I across the capacitor in a purely capacitive AC circuit is

(a)

i_m sin (\(\omega\)t + \(\pi\)/4)

(b)

i_m sin (\(\omega\)t + \(\pi\)/2)

(c)

i_m cos (\(\omega\)t + \(\pi\)/4)

(d)

i_m cos (\(\omega\)t + \(\pi\)/2)

40.

A pure inductor of 25.0 mH is connected to a source of 220 V. Find the inductive reactance if the frequency of the source is 50 Hz.

(a)

785 \(\Omega\)

(b)

6.50 \(\Omega\)

(c)

7.85 \(\Omega\)

(d)

8.75 \(\Omega\)

41.

The inductive reactance is directly proportional to the

(a)

inductance

(b)

frequency of the current

(c)

Both (a) and (b)

(d)

amplitude of current

42.

A resistance of 20 \(\Omega \) is connected to a source of an alternating potential, V = 220 sin (100\(\pi\)t). The time taken by current to change from its peak value to rms value is

(a)

0.2 s

(b)

0.25 s

(c)

25 x 10^-3 s

(d)

2.5 x 10^-3 s

43.

Voltage and current in an ACcircuit are given by
v = 5 sin (100 \(\pi\)t - \(\pi\)/6) and I = 4 sin (l00 \(\pi\)t + \(\pi\)/6)

(a)

voltage leads the current by 30\(\unicode{xb0} \)

(b)

current leads the voltage by 30\(\unicode{xb0} \)

(c)

current leads the voltage by 60\(\unicode{xb0} \)

(d)

voltage leads the current by 60\(\unicode{xb0} \)

44.

Which of the following graphs shows, in a pure resistor, the voltage and current are in phase?

(a)

(b)

(c)

(d)

45.

When a voltage measuring device is connected to AC mains, the meter shows the steady input voltage of 220 V. This means

(a)

input voltage cannot be AC voltage, but a DC voltage

(b)

maximum input voltage is 220 V

(c)

the meter reads not Ybut < V² > and is calibrated to read \(\sqrt{<{V}^{2}>}\)

(d)

the pointer of the meter is stuck by some mechanical defect

46.

If the rms current in a 50 Hz AC circuit is 5 A, the value of the current 1/300 s after its value becomes zero is

(a)

5\(\sqrt{2} A\)

(b)

5\(\sqrt{3/2}\) A

(c)

5 / 6 A

(d)

5 / \(\sqrt{2} A\)

47.

A 50Hz AC current of crest value 1A flows through the primary of a transformer. If the mutual inductance between the primary and secondary be 0.5 H, the creast voltage induced in the secondary is

(a)

75 V

(b)

150 V

(c)

100 V

(d)

none of these

48.

When an AC voltage of 220V is applied to the capacitor C

(a)

the maximum voltage between plates is 220V

(b)

the current is in phase with he applied voltage

(c)

The charge on the plates is in phase with the applied voltage

(d)

power delivered to the capacitor is zero

49.

Electrical energy is transmitted over large distances at high alternating voltages. Which of the following statements is (are) correct?

(a)

For a given power level, there is a lower current

(b)

Lower current implies less power loss

(c)

Transmission lines can be made thinner

(d)

It is easy to reduce the voltage at he receiveing end using step-down transformers

50.

In an alternating current circuit consisting of elements in series, the current increases on increasing the frequency of supply. Which of the following elements are likely to constitute the circuit?

(a)

Only resistor

(b)

Resistor and an inductor

(c)

Resistor and a capacitor

(d)

Only a capacitor

51.

The output of a step-down transformer is measured to be 24V when connected to a 12 watt light blub. The value of the peak current is

(a)

\(1/\sqrt { 2 } A\)

(b)

\(\sqrt { 2 } A\)

(c)

2 A

(d)

\(2\sqrt { 2 } A\)

52.

An induced of reactance 1 and a resistor of 2 are connected in series to the terminals of a 6V(rms) a.c. source. The power dissipated in the circuit is

(a)

8 W

(b)

12 W

(c)

14.4 W

(d)

18 W

53.

Which of the following combinations should be selected for better tuning of an LCR circuit used for communication?

(a)

R = 20\(\Omega \), L = 1.5H, C = 35\(\mu\)F

(b)

R = 25\(\Omega \), L = 2.5H, C = 45\(\mu\)F

(c)

R = 15\(\Omega \), L = 3.5H, C = 30\(\mu\)F

(d)

R = 25\(\Omega \), L = 1.5H, C = 45\(\mu\)F

54.

To reduce the reasonant frequency in an LCR series circuit with a generator

(a)

the generator frequency should be reduced

(b)

another capacitor should be added in parallel to the first

(c)

the iron core of the inductor should be removed

(d)

dielectric in the capacitor should be removed

55.

An alternating current generator has an internal resistance R_g and an internal reactance X_g. It is used to supply power to a passive load consisting of a resistance R_g and a reactance X_L. For maximum power to be delivered from the generator to the load, the value of X_L is equal to

(a)

zero

(b)

X_g

(c)

-X_g

(d)

R_g

56.

Out of the following, choose the wrong statement :

(a)

A transformer cannot work on d.c.

(b)

A transformer cannot change the frequency of a.c.

(c)

A transformer can produce a.c. power

(d)

In a transformer, when a.c. voltage is raised n times, the alternating current reduces to 1/n time.

57.

A battery of 12V is connected to primary of a transformer with turns ratio n_s/n_p= 10. Voltage across secondary would by

(a)

120 V

(b)

1.3 V

(c)

12 V

(d)

Zero

58.

The efficiency of d.c.motor id given by \(\eta \) =

(a)

\(\frac { back \ e.m.f. }{ applied \ e.m.f. } \)

(b)

\(\frac { applied \ e.m.f }{ back \ e.m.f. } \)

(c)

\(back \ e.m.f.\ \times \ applied \ e.m.f.\)

(d)

none of the above

59.

The form factor of an a.c. generated is given by

(a)

\(\frac { { I }_{ av } }{ { I }_{ 0 } } \)

(b)

\(\frac { { I }_{ 0 } }{ { I }_{ av } } \)

(c)

\(\frac { { I }_{ av } }{ { I }_{ v } } \)

(d)

\(\frac { { I }_{ v } }{ { I }_{ av } } \)

60.

The power factor of an a.c. circuit is given by cos \(\phi \)=

(a)

\(\frac { R }{ Z } \)

(b)

\(\frac { Z }{ R } \)

(c)

\(\frac { R }{ { X }_{ L } } \)

(d)

\(\frac { R }{ { X }_{ C } } \)

61.

Q factor of resonance is given by

(a)

\(\frac { 1 }{ R } \sqrt { \frac { L }{ C } } \)

(b)

\(\frac { 1 }{ R } \sqrt { \frac { C }{ L } } \)

(c)

\(\frac { 1 }{ L } \sqrt { \frac { R }{ C } } \)

(d)

\(\frac { 1 }{ C } \sqrt { \frac { L }{ R } } \)

62.

The alternating current from a source is represented by I = 0.5 sin 314t. The frequency of a.c. is

(a)

314 Hz

(b)

100 Hz

(c)

50 Hz

(d)

zero

63.

The average value of a.c. voltage E = E₀ sin \(\omega\)t over the time interval t = 0 to t = \(\pi /\omega \) is

(a)

\(-2{ E }_{ 0 }/\pi \)

(b)

\({ E }_{ 0 }/\pi \)

(c)

\(\frac { 2{ E }_{ 0 } }{ \pi } \)

(d)

zero

64.

The peak value of 220 V a.c. is

(a)

220V

(b)

\(\frac { 220 }{ \sqrt { 2 } } V\)

(c)

440V

(d)

\(220\sqrt { 2 } V\)

Assertion and reason

22 x 1 = 22

65.

Assertion : A laminated core is used in transformers to increase eddy currents.
Reason: The efficiency of a transformer increases with increase in eddy currents.
Codes:
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

66.

Assertion : When the frequency of the AC source in an LCR circuit equals the resonant frequency, the reactance of the circuit is zero, and so there is no current through the inductor or the capacitor.
Reason : The net current in the inductor and capacitor is zero.
Codes:
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

67.

Assertion : The power in an ac circuit is minimum if the circuit has only a resistor.
Reason: Power of a circuit is independent of the phase angle.
Codes:
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

68.

Assertion : In a purely inductive or capacitive circuit, the current is referred to as wattless current.
Reason: No power is dissipated in a purely inductive or capacitive circuit even though a current is flowing in the circuit.
Codes:
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

69.

Assertion : The voltage and current in a series AC circuit are given by V = V₀sinωt and i = i₀cosωt. The power dissipated in the circuit is zero.
Reason : Power in AC circuit is given by P=V₀I₀ cosΦ / 2
Codes:
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

70.

Assertion : The power is produced when a transformer steps up the voltage.
Reason : In an ideal transformer VI = constant.
Codes:
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

71.

Assertion : The inductive reactance limits amplitude of the current in a purely inductive circuit.
Reason: The inductive reactance is independent of the frequency of the current.
Codes:
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

72.

Assertion : The alternating current lags behind the emf by a phase angle of, π/2 when AC flows through an inductor.
Reason : The inductive reactance increases as the frequency of AC source increases.
Codes:
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

73.

Assertion : A capacitor is connected to a direct current source. Its reactance is infinite.
Reason : Reactance of a capacitor is given by χ_c = 1/ωC.
Codes:
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

74.

Assertion : In series LCR resonance circuit, the impedance is equal to the ohmic resistance.
Reason: At resonance, the inductive reactance exceeds the capacitive reactance.
Codes:

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.

(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion

75.

Assertion (A) : A step-up transformer cannot be used as a step-down transformer.
Reason (R) : Atransformer works only in one direction
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.

76.

Assertion (A) : In a series R-L-C circuit, the voltages across resistor, inductor and capacitor are BV, 16V and 10V, respectively. The resultant emf in the circuit is 10 V.
Reason (R) : Resultant emf of the circuit is given by the relation. \(E=\sqrt{V_R^2+\left(V_L-V_C\right)^2}\)
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.

77.

Assertion (A) : If X_C > X_L, φ is positive and the circuit is predominantly capacitive. The current in the circuit leads the source voltage.
Reason (R) : If X_C < X_L, φ is negative and the circuit is predominantly inductive, the current in the circuit lags the source voltage.
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.

78.

Assertion (A) : Phasors V and I for the case of a resistor are in the same direction.
Reason (R) : The phase angle between the voltage and the current is zero.
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.

79.

Assertion (A) : An inductance and a resistance are connected in series with an A.C circuit. In this circuit the current and the potential difference across the resistance lags behind potential difference across the inductance by an angle \(\pi / 2\)
Reason (R) : In L- R circuit voltage leads the current by phase angle which depends on the value of inductance and resistance both.
Codes:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

80.

Assertion (A) : Soft iron is used as a core of transformer.
Reason (R) : Area of hysteresis loop for soft iron is small.
Codes:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

81.

Assertion (A) : A transformer cannot work on D.C supply.
Reason (R) : D.C changes neither in magnitude nor in direction.
Codes:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

82.

Assertion (A) : An electric lamp connected in series with a variable capacitor and A.C source, its brightness increases with increase in capacitance.
Reason (R) : Capacitive reactance decreases with increase in capacitance of capacitor.
Codes:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

83.

Assertion (A) : Long distance transmission of A.C is carried out at extremely high voltage.
Reason (R) : For large distance, voltage has to be large.
Codes:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

84.

Assertion (A) : At resonance, LCR series circuit have a maximum current.
Reason (R) : At resonance, in LCR series circuit, the current and e.m.f are in phase with each other.
Codes:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

85.

Assertion (A) : When capacitive reactance is smaller than the inductive reactance in LCR series circuit, e.m.f. leads the current.
Reason (R) : The phase angle is the angle between the alternating e.m.f and alternating current of the circuit.
Codes:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

86.

Assertion (A) : Capacitor serves as a block for D.C and offers an easy path to A.C
Reason (R) : Capacitive reactance is inversely proportional to frequency.
Codes:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

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Answers Key:

Multiple Choice Question

64 x 1 = 64

(a)
\(\frac{V_0}{\sqrt{2}}\)

(d)
zero

(a)
L, C and R

(d)
\(\sqrt{R^2+\left(X_L-X_C\right)^2}\)

(a)
30 V

(b)
increase

(b)
0.4 A

(b)
127 µF

10.

11.

(a)
\(\frac{15}{\sqrt 2} A\)

12.

13.

(b)
20 mA

14.

15.

(a)
If the frequency of the source is incresed, the impedance of the circuit first decreases and then increases.

16.

17.

(d)
\(\frac{1}{3}\)

18.

19.

(d)
\(\frac{X}{4}\)

20.

(d)
an iron rod is inserted in the coil

21.

(a)
100 mH

22.

23.

24.

(b)
NABω

25.

(a)
reduce the energy loss due to eddy currents

26.

27.

(a)
0.8

28.

(d)
zero

29.

30.

(a)
Inductor and capacitor.

31.

(a)
to oscillate at a' particular frequency

32.

(a)
1 x 10³rad/s

33.

(d)
only resistive

34.

35.

(b)
0.27 A

36.

(d)
L/4

37.

38.

(a)
\(\omega\)CV_m

39.

(b)
i_m sin (\(\omega\)t + \(\pi\)/2)

40.

41.

42.

(d)
2.5 x 10^-3 s

43.

44.

45.

46.

(b)
5\(\sqrt{3/2}\) A

47.

48.

49.

(a)
For a given power level, there is a lower current

50.

51.

(a)
\(1/\sqrt { 2 } A\)

52.

53.

54.

(b)
another capacitor should be added in parallel to the first

55.

56.

57.

(d)
Zero

58.

(a)
\(\frac { back \ e.m.f. }{ applied \ e.m.f. } \)

59.

(d)
\(\frac { { I }_{ v } }{ { I }_{ av } } \)

60.

(a)
\(\frac { R }{ Z } \)

61.

(a)
\(\frac { 1 }{ R } \sqrt { \frac { L }{ C } } \)

62.

63.

64.

(d)
\(220\sqrt { 2 } V\)

Assertion and reason

22 x 1 = 22

65.

(d) Assertion is incorrect, reason is correct.
Explanation:
Large eddy currents are produced in non-laminated iron core of the transformer by the induced emf, as the resistance of bulk iron core is very small. By using thin iron sheets as core the resistance is increased. Laminating the core substantially reduces the eddy currents. Eddy current heats up the core of the transformer. More the eddy currents greater is the loss of energy and the efficiency goes down.

66.

(d) Assertion is incorrect, reason is correct.
Explanation:
The currents in capacitor and in inductor are opposite and so net current is zero.

67.

(d) Assertion is incorrect, reason is correct.

68.

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.

69.

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.

70.

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
Explanation:
Transformer cannot produce power, but it transfer from primary to secondary.

71.

72.

(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion

73.

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.

74.

75.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

76.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion
The resultant emf in the L-C-R circuit is given by
\(\Rightarrow E=\sqrt{V_R^2+\left(V_L-V_C\right)^2} \)
\(\Rightarrow E=\sqrt{(8)^2+(16-10)^2} \)
\(\Rightarrow E=\sqrt{64+36} \)
\(\Rightarrow E=10 \mathrm{~V}\)

77.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

78.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

79.

(b): As both the inductance and resistance are joined in series, hence current through both will be same. But in case of resistance, both the current and potential vary simultaneously, hence they are in same phase. While in case of an inductance when current is zero, potential difference across it is maximum and when current reaches maximum \((\text { at } \omega t=\pi / 2)\) potential difference across it becomes zero i.e., potential difference leads the current by \(\pi / 2\) or current lags behind the potential difference by \(\pi / 2\) Phase angle in case of LR circuit is given as \(\phi=\tan ^{-1}\left(\frac{\omega L}{R}\right)\)

80.

(a): The alternating current flowing through the coils, magnetises and demagnetises the iron core again and again over complete cycles. During each cycle of magnetisation, some energy is lost due to hysteresis, the energy lost during a cycle of magnetisation being equal to area of hysteresis loop (in magnitude). Energy loss can be reduce by selecting the material core, which has narrow hysteresis loop, that is why soft iron core is used.

81.

(a): Transformer works on the principle of mutual induction i.e., if two coils are inductively coupled and when current or magnetic flux is changed through one of the two coils, then induced e.m.f. is produced in the other coil. So whenever there is change in current or magnetic flux, only then e.m.f. is induced. But in case of D.C. current or voltage, e.m.f. is not induced because it remain constant throughout and never changes its direction and magnitude. Therefore transformer cannot work when D.C. is applied.

82.

(a): Capacitive reactance \(X_{C}=\frac{1}{\omega C}\) When capacitance C increases, the capacitive reactance decreases. Due to decrease in its values, the current in the circuit will increase \(\left(I=\frac{\dot{E}}{\sqrt{R^{2}+X_{C}^{2}}}\right)\) and hence brightness of source (or electric lamp) will also increases.

83.

(c): The transmission is done at high voltage due to which current through the wire is reduced By reduction in current corresponding dissipation of energy is also reduced \(\left(\text { as } H \propto I^{2} R\right)\) If transmissioh is done at low voltage then we have to use thick wire-in order to reduce the dissipation of energy. This increase the cost of transmission lines wires. In order to reduce both energy dissipation and cost of transmission wire, transmission is done at high voltage by using step-up transformers.

84.

(b): At resonance \(X_{L}=X_{C} \text { or } \omega L=\frac{1}{\omega C}\) Because of this impedance of LCR series circuit become equal to resistance of circuit \(\left(Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}\right)\).
Therefore from \(I=\frac{E}{Z}=\frac{E}{R},\) at resonance, current in LCR series circuit is maximum. Correspondingly phase angle is also equal to zero. Therefore emf and current are in phase in LCR series circuit.

85.

(b): The phase angle for the LCR series circuit is given by \(\tan \theta=\frac{X_{L}-X_{C}}{R}=\frac{\omega L-1 / \omega C}{R}\)
where X_L, X_C are inductive reactance and capacitive reactance respectively. When \(X_{L}>X_{C}\) then \(\tan \theta\) is positive i.e \(\theta\) is positive (between 0 and \(\pi / 2\)) Hence emf leads the current.

86.

(a): The capacitive reactance of capacitor is given by \(X_{C}=\frac{1}{\omega C}=\frac{1}{2 \pi f C}\)
So this is infinite for D.C (f = 0) and has a finite value for A.C Therefore a capacitor blocks D.C and offers an easy path for A.C.