Explanation

1:N = 1:5 => step-up transformer ✔️

V1/V2 = N1/N2 => 200/V2 = 1/5

V2 = 1000 V (not 40V) ❌

I1/I2 = N2/N1 => 3/I2 = 5/1

I2 = 0.6 A (not 15A) ❌

Explanation

v = 6 cos (100t − 30°)

i = C dv/dt

= 50×10^(-6) × d/dt [6 cos (100t − 30°)]

= 50×10^(-6) × (-6)(100) sin(100t - 30°)

= 30×10^(-3) cos(100t - 30° + 90°)

= 30 cos(100t + 60°) mA

Explanation

Power is the rate of change of energy with respect to time.

Mathematically, P = dW/dt, where W is energy.

Explanation

v²/R = v × (v/R) = v × i

i²/G = i × (i/G) = i × v (since G = 1/R, i/G = v)

So, v²/R = i²/G

Explanation

When the characteristic equation has equal real roots, the RLC circuit is critically damped.

In this case, the circuit returns to steady state as fast as possible without oscillation.

Explanation

A capacitor stores energy in the electric field between its plates.

The energy is proportional to ½ C V², where C is capacitance and V is voltage.

Explanation

1/R_eq = 1/4 + 1/6 + 1/12

= (3 + 2 + 1)/12

= 1/2

R_eq = 2 Ω

V = I × R_eq

= 6 A × 2 Ω

= 12 V

Explanation

f = 60 Hz, C = 50 μF

X_L = 2πfL = 2π(60)(0.2) = 75.4 Ω

X_C = 1 / (2πfC) = 1 / (2π(60)(50×10^(-6))) = 53.05 Ω

Z = √(R² + (X_L - X_C)²)

= √(5² + (75.4 - 53.05)²)

= √(25 + 22.35²)

= √(25 + 499)

≈ 22.9 Ω

Explanation

A_V = g_m × R_C

= 40 × 10^(-3) S × 4 × 10^3 Ω

= 40 × 4

= 160

Explanation

I_C = β × I_B

= 150 × 20 μA

= 150 × 20 × 10^(-6) A

= 3 × 10^(-3) A

= 3.0 mA