Question

Two capacitors \( C_1 \) and \( C_2 \) are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are \( U_1 \) and \( U_2 \), respectively. Which of the given statements is true? 

• A. \( C_1>C_2, U_1<U_2 \)
• B. \( C_2>C_1, U_2>U_1 \)
• C. \( C_2>C_1, U_2<U_1 \)
• D. \( C_1>C_2, U_1>U_2 \)

Hint:

Capacitance affects charging time and the energy stored; a higher capacitance results in slower charging and more energy storage at the same voltage.

Answer 1

The Correct Option is B

From the graph, \( C_2 \) charges slower than \( C_1 \), indicating a higher capacitance \( C_2>C_1 \) as capacitance is inversely proportional to the rate of charging (under constant voltage). Given \( U = \frac{1}{2} C V^2 \), the energy stored \( U \) is directly proportional to \( C \). Thus, \( U_2 \), which is associated with \( C_2 \), would be greater than \( U_1 \).