JEE MAIN - Physics (2025 - 28th January Morning Shift - No. 14)
Two capacitors $\mathrm{C}_1$ and $\mathrm{C}_2$ are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are $\mathrm{U}_1$ and $\mathrm{U}_2$, respectively. Which of the given statements is true?
_28th_January_Morning_Shift_en_14_1.png)
$\mathrm{C}_2>\mathrm{C}_1, \mathrm{U}_2>\mathrm{U}_1$
$\mathrm{C}_1>\mathrm{C}_2, \mathrm{U}_1>\mathrm{U}_2$
$\mathrm{C}_2>\mathrm{C}_1, \mathrm{U}_2<\mathrm{U}_1$
$\mathrm{C}_1>\mathrm{C}_2, \mathrm{U}_1<\mathrm{U}_2$
Explanation
_28th_January_Morning_Shift_en_14_2.png)
Since parallel combination, so v is same for both
we know, $q=cv$
$\Rightarrow q \propto C$ (for constant v)
we can see in the graph,
at final state, $q_2 > q_1$,
so $c_2 > c_1$
Now, as $$u = {1 \over 2}c{v^2} \Rightarrow u \propto c$$ (for constant v)
$$ \Rightarrow {u_2} > {u_1}$$
Hence, option 1 is correct.
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