2022 Electrostatic Potential and CapacitanceSharing of Charge between Capacitors Medium Question 1 of 3 in Sharing of Charge between Capacitors

A capacitor of capacitance C=900 pF is charged fully by 100 V battery B as shown in figure (a). Then…

A capacitor of capacitance $C=900\ pF$ is charged fully by 100 V battery B as shown in figure (a). Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance $C=900\ pF$ as shown in figure (b). The electrostatic energy stored by the system (b) is

A $1.5\times10^{-6}\ J$
B $4.5\times10^{-6}\ J$
C $3.25\times10^{-6}\ J$
D $2.25\times10^{-6}\ J$

The answer is D.

Solution

Common potential $V_c = \frac{C_1V_1 + C_2V_2}{C_1 + C_2} = \frac{C \times 100 + C \times 0}{C + C} = 50$ V Energy stored in system (b) $= 2 \times \frac{1}{2}CV_c^2 = CV_c^2$ $= 900 \times 10^{-12} \times 50 \times 50 = 2.25 \times 10^{-6}$ J

Concept energy after connecting to an uncharged capacitor

Sharing of Charge between Capacitors in past papers

3 questions from this chapter have appeared across 3 exam years.