Question 21.5: Average Power in an RLC Series Circuit Goal Understand power...
Average Power in an RLC Series Circuit
Goal Understand power in R L C series circuits.
Problem Calculate the average power delivered to the series R L C circuit described in Example 21.4.
Strategy After finding the rms current and rms voltage with Equations 21.2 and 21.3,
I_{\mathrm{rms}}={\frac{I_{\mathrm{max}}}{\sqrt{2}}}=0.707I_{\mathrm{max}} (21.2)
\Delta V_{\mathrm{rms}}={\frac{\Delta V_{\mathrm{max}}}{\sqrt{2}}}=0.707\,\Delta V_{\mathrm{max}} (21.3)
substitute into Equation 21.17,
\mathscr{P}_{\mathrm{av}}=I_{\mathrm{rms}}\Delta V_{\mathrm{rms}}\cos\phi (21.17)
using the phase angle found in Example 21.4.
First, use Equations 21.2 and 21.3 to calculate the rms current and rms voltage:
\begin{aligned} I_{\mathrm{rms}} & =\frac{I_{\max }}{\sqrt{2}}=\frac{0.255 \mathrm{~A}}{\sqrt{2}}=0.180 \mathrm{~A} \\ \Delta V_{\mathrm{rms}} & =\frac{\Delta V_{\max }}{\sqrt{2}}=\frac{1.50 \times 10^{2} \mathrm{~V}}{\sqrt{2}}=106 \mathrm{~V} \end{aligned}
Substitute these results and the phase angle \phi=-64.8^{\circ} into Equation 21.17 to find the average power:
\begin{aligned} \mathscr{P}_{\mathrm{av}} & =I_{\mathrm{rms}} \Delta V_{\mathrm{rms}} \cos \phi=(0.180 \mathrm{~A})(106 \mathrm{~V}) \cos \left(-64.8^{\circ}\right) \\ & =8.12 \mathrm{~W} \end{aligned}
Remark The same result can be obtained from Equation 21.16, \mathscr{P}_{\mathrm{av}}=I_{\mathrm{rms}}^{2} R.