Question

A Circuit consists of the resistance of $10\Omega$ and capacitance of $0.1\mu F$. If an alternating emf of $100V,50Hz$ is applied, the current in the circuit is

• A. 3.14 mA
• B. 6.28 mA
• C. 1.51 mA
• D. 7.36 mA

Answer 1

The correct option is A 3.14 mA

$X_C=\frac{1}{2\pi \nu C}=\frac{1}{2\times 3.14\times 50\times 0.1\times {10}^{-6}}$

$=3.2\times {10}^4\Omega$

$Z=\sqrt{R^2+X_C^2}=\sqrt{100+10.28\times {10}^8}=3.2\times {10}^4\Omega$

$I_{rms}=\frac{{\epsilon }_{rms}}{Z}=\frac{100}{3.2\times {10}^4}=3.14\times {10}^{-3}A=3.14mA$