In an L-R circuit, the inductive reactance is equal to 3 times the resistance ' R ' of the circuit. An e.m.f. E=E₀ ( t) is applied to the circuit. The power consumed in the circuit is

Step-by-step solution

Inductive reactance is given as X_L = 3 R . For an L-R circuit, the impedance is Z = R^2 + X_L^2 . Substituting the given reactance yields: Z = R^2 + ( 3 R)^2 = R^2 + 3R^2 = 4R^2 = 2R The RMS voltage is E_ rms = E₀/ 2 , so the RMS current becomes: I_ rms = E_ rms Z = E₀ 2 2R = E₀ 2 2 R The power factor is = R/Z = R/(2R) = 1/2 . Power consumption follows P = E_ rms I_ rms : P = ( E₀ 2 ) ( E₀ 2 2 R ) ( 1 2 ) = E₀^2 8R Verifying with P = I_ rms ^2 R gives the same result: P = ( E₀ 2 2 R )^2 R = E₀^2 8R The power consu