If a coil of inductance L and resistance R is connected to AC source with voltage V and angular frequency and current I, then the inductance L is

Step-by-step solution

The impedance Z of a coil having inductance L and resistance R in an AC circuit is given by Z = R^2 + X_L^2 , where the inductive reactance is X_L = L . From Ohm's law for AC circuits, the impedance is also given by Z = V_ rms I_ rms . Equating the two expressions for impedance: R^2 + ^2 L^2 = V_ rms I_ rms Squaring both sides: R^2 + ^2 L^2 = ( V_ rms I_ rms )^2 Rearranging to solve for ^2 L^2 : ^2 L^2 = ( V_ rms I_ rms )^2 - R^2 Taking the square root of both sides: L = ( V_ rms I_ rms )^2 - R^2 L = 1 ( V_ rms I_