Capacitors in Parallel and in Series — Question 3

Question 3

A mixed network requires branch charge before individual voltage division

One branch between A and B contains 6.00 nF in series with 3.00 nF through neutral M. A separate 4.00 nF capacitor connects A directly to B. Apply VA-VB=12.0 V.

1. Find the equivalent capacitance and total charge delivered to terminal A.

2. Find every capacitor charge and voltage drop.

Question 3 - Solution

A mixed network requires branch charge before individual voltage division

(a) Method and calculation

$$C_s=\frac{6(3)}{6+3}=2.00\,\mathrm{nF},\quad C_{\mathrm{eq}}=C_s+4.00=6.00\,\mathrm{nF}.$$$$Q_A=C_{\mathrm{eq}}V=72.0\,\mathrm{nC}.$$

(b) Interpretation and further calculation

$$Q_s=C_sV=24.0\,\mathrm{nC},\quad V_{6}=24/6=4.00\,\mathrm V,\quad V_{3}=24/3=8.00\,\mathrm V.$$$$Q_4=(4.00)(12.0)=48.0\,\mathrm{nC},\quad V_4=12.0\,\mathrm V.$$

Physical check

The total terminal charge splits between branches; it is not the charge of either series capacitor.