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Electric Oscillations

Problem 4.137

A coil with inductive resistance XL=30ΩX_{L}=30 \Omega and impedance Z=50ΩZ=50 \Omega is connected to the mains with effective voltage value V=100 VV=100 \mathrm{~V}. Find the phase difference between the current and the voltage, as well as the heat power generated in the coil.

Reveal Answer
 4.137. The current lags behind the voltage by the phase angle φ=arccos⁡1−(XL/Z)2≈37∘,P=V2Z2Z2−XL2=0.16 kW\begin{aligned} &\text { 4.137. The current lags behind the voltage by the phase angle }\\ &\varphi=\arccos \sqrt{1-\left(X_{L} / Z\right)^{2}} \approx 37^{\circ}, P=\frac{V^{2}}{Z^{2}} \sqrt{Z^{2}-X_{L}^{2}}=0.16 \mathrm{~kW} \end{aligned}
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