Question

The impedance of a circuit, when a resistance $R$ and an inductor of inductance $L$ are connected in series in an AC circuit of frequency $f$, is

• A. $\sqrt{R+2{\pi }^2{f}^2{L}^2}$
• B. $\sqrt{R+4{\pi }^2{f}^2{L}^2}$
• C. $\sqrt{R^2+4{\pi }^2{f}^2{L}^2}$
• D. $\sqrt{R^2+2{\pi }^2{f}^2{L}^2}$

Answer 1

Answer: (C)

$\sqrt{R^2+4{\pi }^2{f}^2{L}^2}$

The impedance due to the inductor is $2\pi fL$ and voltage drop across inductor leads the voltage drop across resistor by $90°$.

So, the net impedance will be: $Z=\sqrt{R^2+{\left(2\pi fL\right)}^2}$