Question

If 10 mV/ 1kHz input is given to a series RC circuit then the output voltage across the capacitor is

• A. 8.5 mV
• B. 10 mV
• C. 7.5 mV
• D. 6.5 mV

Answer 1

Answer: (A)

8.5 mV

Given : $f=1000Hz$, $R=1000\Omega$ and $C=10nF={10}^{-8}F$

Input voltage $V_1=10\times {10}^{-3}$ volts

Voltage across capacitor $V_c=I{X}_c=\frac{V_{in}}{|Z|}{X}_c$
where $|Z|=\sqrt{R^2+X_c^2}=\sqrt{R^2+\frac{1}{(2\pi fC{)}^2}}$

Also using $X_c=\frac{1}{2\pi f}$
$\therefore V_c=\frac{10\times {10}^{-3}}{\sqrt{({10}^3{)}^2+(\frac{{10}^4}{2\pi }{)}^2}}\times \frac{1}{{10}^{-8}\times {10}^4\times 2\pi }$

$V_c=8.5mV$