First slide

Power in a.c. circuit

Question

A coil has a resistance 10 $Ω$ and an inductance of 0.4 Henry. It is connected to an AC source of 6.5 V, $\frac{30}{π}$ Hz. The average power consumed in the circuit, is :

Moderate

A

$\frac{5}{8} W$
B

$\frac{4}{3} W$
C

$\frac{3}{8} W$
D

$\frac{6}{7} W$

Solution

$X_{L} = ωL = 0.4 x 2 π x \frac{30}{π} = 24 Ω Z = \sqrt{10^{2} + 24^{2}} = 26 Ω V_{avg} = V_{rms} I_{rms} cosϕ = V_{rms} (\frac{V_{rms}}{Z}) (\frac{R}{Z}) = \frac{{RV}^{2}_{rms}}{Z^{2}} = \frac{5}{8} W$

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