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# In a certain series RLC circuit being driven at a frequency of 60.0 Hz, the maximum voltage across the inductor is 2.00 times the maximum voltage across the resistor and 2.00 times the maximum voltage across the capacitor. By what angle does the current lag the generator emf?

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$\textbf{(a)}$ Assume we have an $RLC$ circuit which is driven be a frequency generator, given that $\mathcal{E}_m=30.0$ V and $I=300$ mA. The maximum voltage across the inductor $V_L=2.00V_R=2.00V_C$ where $V_C$ is the voltage across the capacitor and $V_R$ is the voltage across the resistor. The phase angle is given by:

$\tan(\Phi)=\dfrac{X_L-X_C}{R}$

multiply the right hand side by $I/I$, so:

$\tan(\Phi)=\dfrac{IX_L-IX_C}{IR}$

but,

$V_L=IX_L \qquad V_C=IX_C \qquad V_R=IR$

therefore:

$\tan(\Phi)=\dfrac{V_L-V_C}{V_R}$

using $V_L=2.00V_R$ and $V_C=V_R$, to get:

$\tan(\Phi)=\dfrac{2.00V_R-V_R}{V_R}$

$\tan(\Phi)=1$

$\boxed{\Phi=45.0 }$

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