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(A) The power consumed in an $AC$ circuit is given by the formula:$P = V_{rms} I_{rms} \cos\phi$Since $\cos\phi = \frac{R}{Z}$,we have:$P = V_{rms} I_

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$12$

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(A) The power consumed in an $AC$ circuit is given by the formula:$P = V_{rms} I_{rms} \cos\phi$Since $\cos\phi = \frac{R}{Z}$,we have:$P = V_{rms} I_{rms} \left( \frac{R}{Z} ight)$  ..........$(1)$First,calculate the total impedance $Z$ of the circuit:$Z = \frac{V_{rms}}{I_{rms}} = \frac{120}{3} = 40\,\Omega$Now,substitute the values into equation $(1)$:$108 = (120)(3) 	imes \frac{R}{40}$$108 = 360 	imes \frac{R}{40}$$108 = 9R$$R = \frac{108}{9} = 12\,\Omega$Therefore,the resistance in the circuit is $12\,\Omega$.

$A$ resistor and a pure inductor are connected to an $AC$ supply of $120\,V$ and $50\,Hz$. The current in the circuit is $3\,A$. If the power consumed in the circuit is $108\,W$,then the resistance in the circuit is.....$\Omega $

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