Capacitors in Parallel and in Series — Question 5

Question 5

A series voltage rating is limited by the first capacitor to reach its own ceiling

C1=2.00 nF has a 100 V rating; C2=3.00 nF has an 80.0 V rating. They are connected in series with a neutral isolated junction. Ignore leakage and tolerances.

1. Find the greatest common charge allowed by both ratings.

2. Find the maximum total voltage and each capacitor voltage there.

Question 5 - Solution

A series voltage rating is limited by the first capacitor to reach its own ceiling

(a) Method and calculation

$$Q\le C_1V_{1,*}=200\,\mathrm{nC},\quad Q\le C_2V_{2,*}=240\,\mathrm{nC}.$$$$Q_{\max}=200\,\mathrm{nC}.$$

(b) Interpretation and further calculation

$$V_{1}=100\,\mathrm V,\quad V_{2}=200/3=66.6667\,\mathrm V.$$$$V_{\mathrm{total,max}}=166.667\,\mathrm V<100+80\,\mathrm V.$$

Physical check

Adding nameplate voltage ratings is valid only when charge sharing allows both capacitors to reach those limits together.