Question

The reactance of an inductor is 3 o and
resistance of a resistor is 4 Q. They
ries A 10 volt AC source is connected in the
circuit. The power dissipated in the circuit is
000000
10 V
(1) 12 W
(2) 16 W
(3) 20 W
(4) 24 W
letrical​

Answer 1

Given info : The reactance of an inductor 3 ohm and resistance of a resistor 4 ohm are connected in series to the terminal of 10 Volts (rms) AC source.

To find : The power dissipated in the circuit is ...

solution : reactance of inductor, $X_L$ = 3 ohm

resistance of resistor, R = 4 ohm.

∵ impedance of the circuit, Z = $\sqrt{X_L^2+R^2}$

= √(3² + 4²) = 5 ohm

rms voltage of AC source, $V_{rms}$ = 10 volts

Now rms current through circuit, $I_{rms}=\frac{V_{rms}}{Z}$

= 10/5 = 2 A

power factor, cosΦ = R/Z = 4/5

now power dissipation in the circuit, P = $I_{rms}V_{rms}cos\Phi$

= 2A × 10V × 4/5

= 16 W

Therefore the power dissipation in the circuit is 16W. i.e., option (2)