Question

A coil has a resistance of 10 Ω and an inductance of 0.4 henry. It is connected to an AC source of 6.5 V, 30πHz. Find the average power consumed in the circuit.

Answer 1

Average Power Consumed is $\frac {5\omega}{8}$

Explanation:

• Given, R = 10$\Omega$ L = 0.4 Henry

E = 6.5 V, f = 30 Hz

Z = $\sqrt R^2 + \sqrt X_L^2$

= $\sqrt R^2 + (2\pi fL)^2$

• Power = $V_r_m_sI_r_m_scos\phi$

= $6.5 \times \frac {6.5}{Z} \times \frac {R}{Z}$

= $\frac {6.5 \times 6.5 \times 10}{[\sqrt R^2 + (2\pi fL)^2]^2}$

= $\frac {6.5 \times 6.5 \times 10}{10^2 + (2\pi \times \frac {30}{\pi} \times 0.4)^2}$  

= $\frac {6.5 \times 6.5 \times 10}{100 + 576}$

= 0.625 = $\frac {5\omega}{8}$