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