Question 289: AC fundamentals

Question

An e.m.f. $e=E_0 \cos \omega t$ is applied to a circuit containing $L, C$ and $R$ in series where $X_L=3 R$ and $\mathrm{X}_{\mathrm{C}}=\mathrm{R}$. The average power dissipated in the circuit is

Accepted Answer

Net impedance $Z=\sqrt{R^2+\left(X_L-X_Cight)^2}$
$$ \begin{aligned} Z & =\sqrt{R^2+(3 R-R)^2}=\sqrt{R^2+4 R^2} \ & =\sqrt{5} R \ I_{	ext {rms }} & =\frac{E_{	ext {ms }}}{Z}=\frac{E_0 / \sqrt{2}}{\sqrt{5} R}=\frac{E_0}{\sqrt{10} R} \end{aligned} $$
Average power dissipated,
$$ P=I_{	ext {rim }}^2 \cdot R=\left(\frac{E_0}{\sqrt{10} R}ight)^2 R=\frac{E_0^2 R}{10 R^2}=\frac{E_0^2}{10 R} $$

Answer

$\frac{E_0^2}{5 R}$

Answer

$\frac{E_0^2}{10 R}$

Answer

$\frac{\mathrm{E}_0^2}{15 \mathrm{R}}$

Answer

$\frac{E_0^2}{20 R}$

AC fundamentals

An e.m.f. e=E_0 \cos \omega t is applied to a circuit containing L, C and R in series where X_L=3 R and \mathrm{X}_{\mathrm{C}}=\mathrm{R}. The average power dissipated in the circuit is

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