Question

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

• A. $10 V ; 1.2 \times 10^{4} \Omega$
• B. $10^{4} V ; 10^{4} \Omega$
• C. $50 V ; 1.0 \times 10^{4} \Omega$
• D. $10 V ; 10 \Omega$

Answer 1

Answer: (A)

$I_{v}=1.5 mA =1.5 \times 10^{-3} A$
$\omega=300 rad / sec , R =10 k \Omega=10^{4} \Omega$
$C=0.50 \mu F=0.50 \times 10^{-6} F$
$X_{C}=\frac{1}{\omega C}=\frac{1}{300 \times 0.5 \times 10^{-6}}$
$=6.67 \times 10^{3} \Omega$
$Z=\sqrt{R^{2}+X_{c}^{2}}$
$=\sqrt{\left(10^{4}\right)^{2}+\left(6.67 \times 10^{3}\right)^{2}}$
$Z=1.2 \times 10^{4} \Omega$
RMS voltage across the capacitor $=I_{v} X_{c}$
$=1.5 \times 10^{-3} \times 6.67 \times 10^{3}=10 V$