Question

Two parallel plate capacitors A and B having capacitances of $1\mu F$ and $5\mu F$ are charged separately to the same potential of $100$V. Now the positive plate of A is connected to the negative plate of B and the negative plate of A to the positive plate of B. The final charge on each capacitor is?

• A. $\frac{200}{3}\mu C,\frac{1000}{3}\mu C$
• B. $\frac{100}{3}\mu C,\frac{500}{3}\mu C$
• C. $\frac{250}{3}\mu C,\frac{750}{3}\mu C$
• D. None of these

Answer 1

The correct option is A $\frac{200}{3}\mu C,\frac{1000}{3}\mu C$

According to the scheme of connections,
$V=\frac{C_1{V}_1\sim C_2{V}_2}{(C_1+C_2)}$ (The sign $\sim$ shows difference)
or $V=\frac{({10}^{-6}\times 100)\sim (5\times {10}^{-6}\times 100)}{1\times {10}^{-6}+5\times {10}^{-6}}$ volt
or $V=\frac{400\times {10}^{-6}}{6\times {10}^{-6}}=\frac{400}{6}=\frac{200}{3}$volt
$\therefore Q_1=C_{1}V=(1\times {10}^{-6})\times \left(\frac{200}{3}\right)$
$=\frac{200}{3}\times {10}^{-6}$ coulomb
or $Q_1=\frac{200}{3}\mu C$
Similarly, $Q_2=C_{2}V$
or $Q_2=(5\times {10}^{-6})\times \frac{200}{3}=\frac{1000}{3}\times {10}^{-6}$ coulomb
or $Q_2=\frac{1000}{3}\mu C$.