If the charge on the capacitor is increased by 2C, the energy stored in it increases by 21% . The original charge on the capacitor is

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Let the original charge on the capacitor be $Q$ and its capacitance be $C$ .

The initial energy stored in the capacitor is $U = \frac{Q ^{2}}{2 C}$ .

When the charge is increased by $2$ C, the new charge is $Q^{'} = Q + 2$ .

The new energy stored is $U^{'} = \frac{( Q + 2 ) ^{2}}{2 C}$ .

Given that the energy increases by $21%$ , we have $U^{'} = 1.21 U$ .

Substituting the expressions for $U$ and $U^{'}$ , we get:

$\frac{( Q + 2 ) ^{2}}{2 C} = 1.21 (\frac{Q ^{2}}{2 C})$

$(Q + 2)^{2} = 1.21 Q^{2}$

Taking the square root on both sides:

$Q + 2 = 1.1 Q$

$0.1 Q = 2$

$Q = 20$ C

Answer: 20 C

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