Question

Consider the situation of the previous problem. Find the average electric field energy stored in the capacitor and the average magnetic field energy stored in the coil.

Answer 1

Given:
Resistance in the LCR circuit, R = 300 Ω
Capacitance in the LCR circuit, C = 20 μF = 20 × 10⁻⁶ F
Inductance in the LCR circuit, L = 1 henry
Net impedance of the LCR circuit, Z = 500 ohm
RMS value of voltage, ${\epsilon }_{\mathrm{rms}}$ = 50 V
RMS value of current, I_rms = 0.1 A
Peak current $\left(I_0\right)$ is given by,
$I_0=\frac{E_{\mathrm{rms}}\sqrt{\mathit{2}}}{Z}=\frac{50\times 1.414}{500}=0.1414\mathrm{A}$
Electrical energy stored in capacitor$\left(U_C\right)$ is given by,
$U_C=\frac{1}{2}C{V}^2$
$$\begin{gathered} \Rightarrow U_C=\frac{1}{2}\times 20\times {10}^{-6}\times 50\times 50 \\ \Rightarrow U_C=25\times {10}^{-3}\mathrm{J}=25\mathrm{mJ} \end{gathered}$$
Magnetic field energy stored in the coil $\left(U_L\right)$ is given by,
$U_L=\frac{1}{2}L{I}_0^2$
$$\begin{gathered} \Rightarrow U_L=\frac{1}{2}\times 1\times {\left(0.1414\right)}^2 \\ \Rightarrow U_L\approx 5\times {10}^{-3}\mathrm{J} \\ \Rightarrow U_L=5\mathrm{mJ} \end{gathered}$$