Board-style MCQs and past-paper numericals in the BIEK / Sindh Board pattern. Tap an option to check yourself instantly. Solved questions are at the bottom.
Multiple-choice questions
Solved numericals (past papers)
Peak value from the rms value
The rms voltage of the mains is 220 V. Find the peak (maximum) voltage.
V₀ = √2 × V_rms = 1.414 × 220 = 311 V
Inductive reactance
A 0.5 H inductor is connected to a 50 Hz supply. Find its inductive reactance. (ω = 2πf)
X_L = ωL = 2πf L = 2 × 3.14 × 50 × 0.5
= 157 Ω
Capacitive reactance
A 50 μF capacitor is connected to a 50 Hz supply. Find its capacitive reactance.
X_C = 1/(ωC) = 1/(2πf C) = 1/(2 × 3.14 × 50 × 50 × 10⁻⁶)
= 1/(0.0157) = 63.7 Ω
Impedance of a series RLC circuit
A series circuit has R = 30 Ω, X_L = 80 Ω and X_C = 40 Ω. Find the impedance Z.
Z = √[R² + (X_L − X_C)²] = √[30² + (80 − 40)²]
= √[900 + 1600] = √2500 = 50 Ω
Resonant frequency of an LC circuit
A circuit has L = 2 H and C = 8 μF. Find the resonant frequency f₀.
f₀ = 1/(2π√(LC)) = 1/(2π√(2 × 8 × 10⁻⁶))
= 1/(2π√(16 × 10⁻⁶)) = 1/(2π × 4 × 10⁻³) = 1/(0.0251)
= 39.8 Hz
Average power in an AC circuit
An AC circuit carries V_rms = 200 V and I_rms = 5 A with a phase angle φ = 60° (cos60° = 0.5). Find the average power.
P = V_rms I_rms cosφ = 200 × 5 × 0.5 = 500 W