Capacitance — Question 3

Question 3

A common voltage offset leaves a two-terminal capacitor unchanged

An ideal capacitor has C=2.50 nF, $V_A=80$ V and $V_B=30$ V. Neglect coupling to all other objects.

1. Find the plate charges.

2. Raise both terminal potentials by 200 V. Find the new charge and explain which assumption makes this common-mode change irrelevant.

Question 3 - Solution

A common voltage offset leaves a two-terminal capacitor unchanged

(a) Method and calculation

$$v=V_A-V_B=50.0\,\mathrm V.$$$$q_A=Cv=125\,\mathrm{nC},\quad q_B=-125\,\mathrm{nC}.$$

(b) Interpretation and further calculation

$$v\prime=(80+200)-(30+200)=50.0\,\mathrm V.$$$$q_A\prime=Cv\prime=q_A,\quad\Delta q_A=0.$$

Physical check

Real terminals may couple capacitively to ground; those extra couplings are explicitly excluded from this two-terminal model.