Question

in a parallel plate capacitor with air between the plates,each plate has an area of 5 x 10^-3m² and the separation between the plates is 2.5mm.

(i) calculate the capacitance of the capacitor .

(ii) if this capacitor is connected to 100V supply ,what would be the charge on each plate ?

(iii) how would charge on the plate be affected ,if a 2.5mm thick mica sheet of k = 8 is inserted between the plates while the voltage supply remains connected?

Answer 1

$$\begin{gathered} 1)Capaci\tan ceofthecapacitorisgivenby: \\ C=\frac{{\epsilon }_{o}A}{d} \\ A=5\times {10}^{-3}{m}^2 \\ d=2.5\times {10}^{-3}m \\ C=\frac{8.85\times {10}^{-12}\times 5\times {10}^{-3}}{2.5\times {10}^{-3}} \\ C=17.7\times {10}^{-12}farad \\ 2)Q=CV \\ Q=17.7\times {10}^{-12}\times 100 \\ Q=17.7\times {10}^{-10}C \\ 3)whenmicasheetintroducedbetweenthecapacitor \\ capaci\tan ceincreases. \\ {C}^{\text{'}}=kC \\ {C}^{\text{'}}=8\times 17.7\times {10}^{-12} \\ {C}^{\text{'}}=61.6\times {10}^{-12}farad \\ Ascapaci\tan ceincreases,chargestoredinthecapacitorincreases. \\ {Q}^{\text{'}}=C^{\text{'}}V=61.6\times {10}^{-12}\times 100 \\ {Q}^{\text{'}}=61.6\times {10}^{-10}C \end{gathered}$$