Published by:
CGP EDU Academic Team
Published on: September 12, 2026
The combination of capacitors with $c_1 = 3 \mu F, c_2 = 4 \mu F$ and $C_3 = 2 \mu F$ is charged by connecting AB to a battery. Consider the following statements
(I) Energy stored in $C_1$ = Energy stored in $C_2$ + Energy stored in $C_3$
(II) Charge on C 1 = Charge on C 2 + Charge on C 3
(III) Potential drop across C 1 = Potential drop across C 2 = Potential drop across C 3
Which of these is/are correct

Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Analyze the circuit. Capacitors C1, C2, and C3 are connected in a configuration where C1 is in series with a parallel combination of C2 and C3.
Step 2: Statement (I): Energy stored in C1 is given by \( U_1 = \frac{1}{2} C_1 V_1^2 \), and the total energy is \( U = U_1 + U_2 + U_3 \) where U2 and U3 are the energies stored in C2 and C3 respectively. This is true as per energy conservation laws.
Step 3: Statement (II): In the series arrangement of capacitors, the charge (Q) on every capacitor remains the same. Thus, \( Q_{C1} = Q_{C2} + Q_{C3} \) also holds true since the total charge divides across parallel paths. Therefore, statement II is also correct.
Step 4: Statement (III): This statement is incorrect as the potential drop across capacitors in series is not equal; for capacitors in parallel, they have the same potential difference.
Thus, the correct options are I and II.
Therefore, the correct answer is A.
Step 2: Statement (I): Energy stored in C1 is given by \( U_1 = \frac{1}{2} C_1 V_1^2 \), and the total energy is \( U = U_1 + U_2 + U_3 \) where U2 and U3 are the energies stored in C2 and C3 respectively. This is true as per energy conservation laws.
Step 3: Statement (II): In the series arrangement of capacitors, the charge (Q) on every capacitor remains the same. Thus, \( Q_{C1} = Q_{C2} + Q_{C3} \) also holds true since the total charge divides across parallel paths. Therefore, statement II is also correct.
Step 4: Statement (III): This statement is incorrect as the potential drop across capacitors in series is not equal; for capacitors in parallel, they have the same potential difference.
Thus, the correct options are I and II.
Therefore, the correct answer is A.
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