Question

An alternating current of frequency ' f ' is flowing in a circuit containing a resistance R and a choke L in series. The impedance of this circuit is
(a) R + 2πfL
(b) $\sqrt{R^2+4\pi^2 f^2L^2}$
(c) $\sqrt{R^2+L^2}$
(d) $\sqrt{R^2\pi fL}$

Answer 1

answer : option (b) $\sqrt{R^2+4\pi^2 f^2L^2}$

explanation :

it is given that, frequency of alternating current is f , resistance of resistor is R and inductance of inductor is L . both inductor and resistor are connected in series in ac circuit.

so, the impedance of a circuit is given by, $Z=\sqrt{R^2+X_L^2}$

inductive reactance, $X_L=2\pi fL$

so, the impedance of this circuit is $Z=\sqrt{R^2+(2\pi fL)^2}$

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

hence, option (b) is correct.