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 ${\displaystyle \varphi }$  .....(i)

I_rms = ${\displaystyle \frac{E_{rms}}{Z}}$

Z = ${\displaystyle \sqrt{R^2+X_L^2}}$

= ${\displaystyle \sqrt{4+1}=\sqrt{5}}$

I_rms = ${\displaystyle \frac{6}{\sqrt{5}}A}$

${\displaystyle \cos \varphi =\frac{6}{\sqrt{5}}A}$

P_av = ${\displaystyle 6\times \frac{6}{\sqrt{5}}\times \frac{2}{\sqrt{5}}}$  .....[From equation (i)]

= ${\displaystyle \frac{72}{\sqrt{5}\sqrt{5}}=\frac{72}{5}}$ = 14.4 W