Explanation

q = 5t sin 4πt mC

i = dq/dt

= d/dt (5t sin 4πt)

= 5 sin 4πt + 20πt cos 4πt (mC/s)

At t = 0.5 s:

i = 5 sin 2π + 10π cos 2π

= 0 + 10π mA

≈ 31.42 mA

Explanation

Z_Th = 80 + j55 Ω

For max power transfer, Z_L = Z_Th*

= 80 - j55 Ω

Explanation

A filter passes signals of certain frequencies while blocking or attenuating others.

Filters can be low-pass, high-pass, band-pass, or band-stop depending on the application.

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