Power in Alternating-Current Circuits — Question 6

Question 6

Series and parallel correction have different effects on a fixed-voltage RL load

A series RL load has R=12.0 ohms and inductive reactance 16.0 ohms at the source frequency. The ideal source is 20.0 V rms. Compare adding a series capacitor that cancels reactance with adding a shunt capacitor that corrects source power factor.

1. Find original current and real power, then find them after series cancellation.

2. Find real load power and source current after ideal shunt correction.

Question 6 - Solution

Series and parallel correction have different effects on a fixed-voltage RL load

(a) Method and calculation

$$Z=\sqrt{12^2+16^2}=20\,\Omega\Rightarrow I=1.00\,A,\quad P=12.0\,W.$$$$\boxed{I_{\mathrm{series}}=20/12=1.66667\,A,\quad P_{\mathrm{series}}=20^2/12=33.3333\,W}.$$

(b) Interpretation and further calculation

$$\text{Shunt correction preserves }V_{\mathrm{load}}=20.0\,V\Rightarrow P_{\mathrm{shunt}}=12.0\,W.$$$$\boxed{I_{s,\mathrm{shunt}}=P/V=.600\,A}.$$

Physical check

Series compensation changes the load branch current; parallel compensation at fixed voltage changes the source current without changing that branch.