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 $\mathrm{C_3}$
(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: Analyzing the circuit configuration, it shows capacitors C1, C2 in parallel with C3.
Step 2: For parallel capacitors, voltage across each capacitor is the same. This verifies statement (III).
Step 3: The total charge stored in the system is equal to the sum of the charge on each capacitor. Therefore, the charge on C1 is equal to the sum of the charges on C2 and C3, supporting statement (II).
Step 4: The energy stored in a capacitor is given by the formula \( U = \frac{1}{2}CV^2 \). For the entire combination, the energy distribution can be expressed as the sum of individual energy storage. Therefore, statement (I) is also correct: Energy stored in C1 = Energy stored in C2 + Energy stored in C3.
Thus, all statements (I, II, and III) are correct.
Therefore, the answer is A: I and II.
Step 2: For parallel capacitors, voltage across each capacitor is the same. This verifies statement (III).
Step 3: The total charge stored in the system is equal to the sum of the charge on each capacitor. Therefore, the charge on C1 is equal to the sum of the charges on C2 and C3, supporting statement (II).
Step 4: The energy stored in a capacitor is given by the formula \( U = \frac{1}{2}CV^2 \). For the entire combination, the energy distribution can be expressed as the sum of individual energy storage. Therefore, statement (I) is also correct: Energy stored in C1 = Energy stored in C2 + Energy stored in C3.
Thus, all statements (I, II, and III) are correct.
Therefore, the answer is A: I and II.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
Two identical capacitors are joined in parallel, charged to a potential V and then separated and th…
The condensers of capacity $C_{1}$ and $C_2$ are connected in parallel, then the equivalent capacit…
A parallel plate capacitor is made by stacking n equally spaced plates connected alternately. If th…
Seven capacitors each of capacity $2 \mu F$ are to be so connected to have a total capacity $\frac{…
The capacitor of capacitance $4 \mu \mathbf{F}$ and $6 \mu F$ are connected in series. A potential …
A parallel plate capacitor with air as medium between the plates has a capacitance of $10 \mu \math…