Question

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

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

Answer 1

The correct option is A $1.2\times {10}^4\Omega ;10V$

$V_{rms}$ across capacitor$=I_{rms}\times C$

$=1.5\times {10}^{-3}\times \frac{1}{\omega C}$

$=1.5\times {10}^{-3}\times \frac{1}{300\times 0.5\times {10}^{-6}}$

$=1\times 10$

$10V$

Impedance of circuit is

$Z=\sqrt{R^2+X_C^2}$

$=\sqrt{({10\times {10}^3)}^2+({\frac{1}{1.5\times {10}^{-4}})}^2}$

$=\sqrt{{10}^8+\frac{{10}^8}{({1.5)}^2}}$

$=1.2\times {10}^4\Omega$