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?
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Capacitance affects charging time and the energy stored; a higher capacitance results in slower charging and more energy storage at the same voltage.
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 \( U_1 \).
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