\(N_z=300, N_s=1200, R_p=0.82 \Omega, R_s=6.2 \Omega,  \)
\(\text {Output power }=32 \mathrm{~kW}, \mathrm{~V}_{\mathrm{s}}=1600 \mathrm{~V}, \eta=80 \%  \)
\(V_s I_s=32000 \mathrm{~W}  \)
\(1600 \times I_s=32000  \)
\(\therefore I_s=\frac{32000}{1600}  \)
\(I_s=20 \mathrm{~A}\)    ......(1)
∴ Power loss in secondary coil \(P  =I_{\mathrm{s}}^2 \times R_{\mathrm{s}}  \)    ......(2)
\(=(20)^2 \times 6.2  \)
\(=400 \times 6.2=2480.0  \)
\(=2480 \mathrm{~W}=2.48 \mathrm{~kW}\)
∴ Power loss in secondary coil P = 2.48 kW   ......(3)
Efficiency \( \eta  =\frac{V_s I_s}{V_P I_P} \)
\(\therefore \frac{80}{100}  =\frac{32 \times 10^3}{V_P I_P}  \)
\(\therefore V_P I_p =\frac{32 \times 10^3 \times 100}{80}  \)
\(=\frac{3200 \times 10^3}{80}  \)
\(V_P I_P =40 \times 10^3 \mathrm{~W}\)     ......(4)
We know that, \(\frac{N_p}{N_s}=\frac{V_P}{V_S}\)     ......(5)
\(\frac{300}{1200}=\frac{V_p}{1600} \Rightarrow V_p  =\frac{300 \times 1600}{1200}  \)
\(=400 \mathrm{~V}\)     ......(6)
From (4), V_pI_p = 40 x 10³
400 I_p = 40 x 10³
\(\therefore I_p =\frac{40 \times 10^3} { 400}={100A}   \)
∴ Power loss in the primary coil = I²_pR_p
= (100)² x 0.82
= 10⁴ x 0.82 = 8200 W
∴ Power loss in the primary coil = 8.2 kW

Magnitude of induced \(\mathrm{emf}|\mathrm{e}|=\left|-\frac{d \phi}{d t}\right|\)
\(\therefore c=\frac{d \phi}{d t}\)
(i) In the region ab,
\(c_1=\frac{d \phi_1}{d t}=\frac{4-0}{1-0}=\frac{4}{1}=4 \mathrm{~V}\)
(ii) In the region bc,
\(c_2=\frac{d \phi_2}{d t}=\frac{4-4}{3-1}=\frac{0}{2}=0 \mathrm{~V}\)
(iii) In the region cd,
\(e_3=\frac{d \phi_2}{d t}=\frac{4-2}{4-3}=\frac{2}{1}=2 \mathrm{~V}\)
(iv) In the region de,
Hence,
\(e_4=\frac{d \phi_4}{d t}=\frac{2-0}{7-4}=\frac{2}{3}=0.66 V  \)
\(\mathrm{e}_2<\mathrm{e}_4<\mathrm{e}_3<\mathrm{e}_1\)
In the ascending order of the magnitude of induced emf
Region bc < Region de < Region cd < Region ab.

The direction of induced current is, a → b, b → c, c → d and d → a

In the inductor voltage leads current by 90°

In the capacitor current leads voltage by 90°

Hence in series LC circuit, the voltage across L and C are 180° out of phase

For capacitor:

The charge decays exponentially with time. When the capacitor discharge.
For Inductor: