(a) A parallel plate capacitor is charged by an ac source. Show that the sum of conduction current ( I_c ) and the displacement current ( I_d ) has…

a) Showing that \(\displaystyle \left(\mathrm{I}_{\mathrm{c}}+\mathrm{I}_{\mathrm{d}}\right)\) has the same value.

b) Explanation of Kirchhoff's first rule at each plate of capacitor.

a) ∵ Total current \(\displaystyle \mathrm{I}=\mathrm{I}_{\mathrm{c}}+\mathrm{I}_{\mathrm{d}}\) outside the capacitor \[\begin{gathered} \mathrm{I}_{\mathrm{d}}=0 \\ \therefore \mathrm{I}=\mathrm{I}_{\mathrm{c}} \end{gathered} \] Inside the capacitor \[\mathrm{I}_{\mathrm{c}}=0 \]