Question

An inductor of reactance 1 Ω and a resistor of 2 Ω are connected in series to the terminals of a 6 V (rms) a.c. source. The power dissipated in the circuit is ______.

Options

• 8 W

• 2 W

• 14.4 W

• 18 W

Answer 1

An inductor of reactance 1 Ω and a resistor of 2 Ω are connected in series to the terminals of a 6 V (rms) a.c. source. The power dissipated in the circuit is 14.4 W.

Explanation:

According to the problem, XL = 1 Ω, R = 2 Ω, Ems = 6 V, P_av = ?

Average power dissipated in the circuit

P_av = E_rmsI_rms cos `phi`  .....(i)

I_rms = `E_(rms)/Z`

Z = `sqrt(R^2 + X_L^2)`

= `sqrt(4 + 1) = sqrt(5)`

I_rms = `6/sqrt(5) A`

`cos phi = 6/sqrt(5) A`

P_av = `6 xx 6/sqrt(5) xx 2/sqrt(5)`  .....[From equation (i)]

= `72/(sqrt(5)sqrt(5)) = 72/5` = 14.4 W