An inductor of inductance L and a resistor of | vedclass

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(B) The impedance $Z$ of an $LR$ series circuit is given by $Z = \sqrt{R^2 + X_L^2} = \sqrt{R^2 + (\omega L)^2} = \sqrt{R^2 + \omega^2 L^2}$.Power dis

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$\frac{V^2 R}{R^2 + \omega^2 L^2}$

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(B) The impedance $Z$ of an $LR$ series circuit is given by $Z = \sqrt{R^2 + X_L^2} = \sqrt{R^2 + (\omega L)^2} = \sqrt{R^2 + \omega^2 L^2}$.Power dissipated in an $AC$ circuit is given by $P = V_{rms} I_{rms} \cos \phi$.Since $I_{rms} = \frac{V_{rms}}{Z}$ and the power factor $\cos \phi = \frac{R}{Z}$, we substitute these into the power formula:$P = V_{rms} \left( \frac{V_{rms}}{Z} \right) \left( \frac{R}{Z} \right) = \frac{V_{rms}^2 R}{Z^2}$.Substituting $Z^2 = R^2 + \omega^2 L^2$, we get:$P = \frac{V^2 R}{R^2 + \omega^2 L^2}$.

An inductor of inductance $L$ and a resistor of resistance $R$ are joined in series and connected to a source of frequency $\omega$. The power dissipated in the circuit is

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