Question

In an AC circuit, an alternating voltage $\epsilon =200\sqrt{2}\sin \left(100t\right)V$ is connected to a capacitor of capacitance $1\mu F$. The value of the current in the circuit is

• A. $10mA$
• B. $100mA$
• C. $200mA$
• D. $20mA$

Answer 1

The correct option is D $20mA$

The given equation of alternating voltage is
$\epsilon =200\sqrt{2}\sin \left(100t\right)V$ ....(i)
The standard equation of alternating voltage is
$\epsilon ={\epsilon }_0\sin \left(\omega t\right)$ ....(ii)
Comparing (i) and (ii), we get
${\epsilon }_0=200\sqrt{2}V,\omega =100rad{s}^{-1}$
The capacitive reactance is
$X_C=\frac{1}{\omega C}=\frac{1}{100\times 1\times {10}^{-6}}\Omega$
The r.m.s. value of current in the circuit is
$i_{rms}=\frac{V_{rms}}{X_C}=\frac{\frac{e_0}{\sqrt{2}}}{\frac{1}{\omega C}}=\frac{\left(}{\frac{200\sqrt{2}}{\sqrt{2}}}=20mA$