Capacitance — Question 1

Question 1

A charge-voltage measurement fixes capacitance independently of operating voltage

An ideal linear two-terminal capacitor has charges $\pm36.0$ nC at potential difference 12.0 V. Its geometry and medium remain fixed.

1. Find C and the charge magnitude at 20.0 V.

2. Find the voltage change when an additional 9.00 nC is transferred from the negative plate to the positive plate, starting from the original state.

Question 1 - Solution

A charge-voltage measurement fixes capacitance independently of operating voltage

(a) Method and calculation

$$C=Q/V=36.0/12.0=3.00\,\mathrm{nF}.$$$$Q(20.0\,\mathrm V)=CV=60.0\,\mathrm{nC}.$$

(b) Interpretation and further calculation

$$\Delta V=\Delta Q/C=9.00/3.00=3.00\,\mathrm V.$$$$V_f=15.0\,\mathrm V,\quad Q_f=45.0\,\mathrm{nC}.$$

Physical check

Changing the operating charge and voltage in proportion does not change a fixed linear capacitance.