Question

A resistor of \(10\,\Omega\) and an inductor of \(0.1\,\text{H}\) are connected in series to a \(100\ \text{V}, 50\ \text{Hz}\) AC source. The impedance of the circuit is:

• A. \(10\,\Omega\)
• B. \(\sqrt{100+100\pi^2}\,\Omega\)
• C. \(\sqrt{100+10000\pi^2}\,\Omega\)
• D. \(100\,\Omega\)

Hint:

Impedance in RL circuit: \(Z=\sqrt{R^2+X_L^2}\).

Answer 1

The Correct Option is B

\[ X_L = 2\pi f L = 2\pi(50)(0.1)=10\pi \] \[ Z=\sqrt{R^2+X_L^2}=\sqrt{10^2+(10\pi)^2}=\sqrt{100+100\pi^2} \]