Question

The charge of a parallel plate capacitor is varying as $q=q_{0} \,sin2\pi\upsilon t$. The plates are very large and close together. Neglecting edge effects, the displacement current through the capacitor is

• A. $\frac{q}{A\varepsilon_{0}}$
• B. $\frac{q}{\varepsilon_{0}} sin2\pi\upsilon t$
• C. $2\pi\upsilon q_{0}\, cos2\pi\upsilon t$
• D. $\frac{2\pi\upsilon q_{0}}{\varepsilon_{0}} cos2\pi\upsilon t.$

Answer 1

Answer: (C)

$I=\frac{dq}{dt}=\frac{d}{dt}\,\left(q_{0}\,sin2\pi vt\right)=q_{0}\,2\pi v\,cos2\pi vt$