Question

In a series $L$-$R$ circuit ($L = 35\, mH$ and $R = 11\,\Omega$), a variable emf source ($V = V_0\, sin\, \omega t$) of $V_{rms} = 220\,V$ and frequency $50\,Hz$ is applied. The current amplitude in the circuit is

• A. $10\,A$
• B. $20\,A$
• C. $30\,A$
• D. $40\,A$

Answer 1

Answer: (B)

$X_{L}=\omega L=\left(2\pi \times 50\right)\left(35 \times 10^{-3}\right)=11\,\Omega$
$\therefore $ Impedance $Z =\sqrt{R^{2}+X^{2}_{L}}; Z=\sqrt{\left(11\right)^{2}+\left(11\right)^{2}}=11\sqrt{2}\,\Omega$
$\therefore I_{0}=\frac{V_{0}}{Z}=\frac{V_{rms} \times \sqrt{2}}{11\sqrt{2}}$
$=\frac{220}{11}$
$=20\,A$