Question

Which integral represents the total work done in charging a capacitor from zero charge to final charge \(Q\)?

Options

• \[W=\int_0^Q Cq\,dq\]

• \[W=\int_0^Q\frac{q}{C}\,dq\]

• \[W=\int_0^Q\frac{C}{q}\,dq\]

• \[W=\int_0^Q\frac{Q}{C}\,dQ\]

Answer 1

During charging, the potential difference at charge \(q\) is \(\frac{q}{C}\), so the incremental work is \(\frac{q}{C}\,dq\). Integrating this from zero charge to final charge \(Q\) gives the total work.