Capacitance — Question 4

Question 4

An offset charge measurement separates capacitance from instrument zero error

A linear capacitor is measured with an instrument obeying $q_{\mathrm{read}}=Cv+q_0$. Readings are 26.0 nC at 4.00 V and 62.0 nC at 10.0 V.

1. Infer C and the offset q0.

2. Predict the reading at -3.00 V and compare the actual plate charge with the reading.

Question 4 - Solution

An offset charge measurement separates capacitance from instrument zero error

(a) Method and calculation

$$C=\frac{62.0-26.0}{10.0-4.00}=6.00\,\mathrm{nF}.$$$$q_0=26.0-(6.00)(4.00)=2.00\,\mathrm{nC}.$$

(b) Interpretation and further calculation

$$q_{\mathrm{read}}(-3.00\,\mathrm V)=-18.0+2.00=-16.0\,\mathrm{nC}.$$$$q_A=Cv=-18.0\,\mathrm{nC}\ne q_{\mathrm{read}}.$$

Physical check

The slope removes a constant measurement offset; a single ratio qread/v would not.