Question

An alternating current of 1.5 mA and angular frequency 300 rad/sec flows through a 10 k Ω resistor and a 0.50 µF capacitor in series. Find the rms voltage across the capacitor and impedance of the circuit.

Options

• 10 V; 1.2 × 10⁴ Ω

• 10⁴ V; 10⁴ Ω

• 50 V; 1.0 × 10⁴ Ω

• 10 V; 10 Ω

Answer 1

10 V; 1.2 × 10⁴ Ω

Explanation:

I_v = 1.5 mA = 1.5 × 10^-3 A

ω = 300rad/sec, R = 10 kΩ = 10⁴ Ω

C = 0.50 μF = 0.50 × 10^-6 F

`"X"_"c" = 1/(omega "C")`

`= 1/(300 xx 0.5 xx 10^-6)`

`= 6.67 xx 10^3 Omega`

Z = `sqrt("R"^2 + "X"_"C"^2) = sqrt((10^4)^2 + (6.67 xx 10^3)^2)`

Z = 1.2 × 10⁴ Ω

RMS voltage across the capacitor = I_vX_C

= 1.5 × 10^-3 × 6.67 × 10³

= 10 V