Question

Evaluating the work integral for charging a capacitor from \(0\) to \(Q\) gives which result?

Options

• \[W=\frac{Q^2}{C}\]

• \[W=\frac{Q}{2C}\]

• \[W=\frac{Q^2}{2C}\]

• \[W=\frac{C}{2Q^2}\]

Answer 1

Evaluating \(\frac{1}{C}\int_0^Q q\,dq\) gives \(\frac{1}{C}\left[\frac{q^2}{2}\right]_0^Q\). Therefore, the work done is \(W=\frac{Q^2}{2C}\).