Three Simple Circuits — Question 9

Question 9

A triangular capacitor voltage produces a square current waveform

An ideal capacitor C is driven by a continuous symmetric triangular voltage between -Vp and +Vp with period T. Its rises and falls each occupy T/2.

1. Find the current in each half-cycle and its rms value.

2. Find the charge transferred during a rising half-cycle and the peak stored energy.

Question 9 - Solution

A triangular capacitor voltage produces a square current waveform

(a) Method and calculation

$$\dot v=\pm\frac{2V_p}{T/2}=\pm4V_p/T.$$$$\boxed{i=\pm4CV_p/T,\quad I_{\mathrm{rms}}=4CV_p/T}.$$

(b) Interpretation and further calculation

$$\Delta q=C\Delta v=2CV_p.$$$$\boxed{U_{\max}=CV_p^2/2}.$$

Physical check

Voltage is continuous at the corners, so current has finite jumps rather than impulse spikes.