A capacitor is charged with a battery and the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Initially,the capacitor of capacitance $C$ is charged to a potential $V$ by a battery. The energy stored is $U = \frac{1}{2} CV^2 = \frac{Q^2}{2C}

Vedclass · Accepted Answer

$\frac{U}{4}$

Vedclass · Answer

(B) Initially,the capacitor of capacitance $C$ is charged to a potential $V$ by a battery. The energy stored is $U = \frac{1}{2} CV^2 = \frac{Q^2}{2C}$,where $Q$ is the initial charge.When the battery is disconnected and an identical capacitor $C$ is connected in parallel,the total charge $Q$ is redistributed between the two capacitors.Since the capacitors are in parallel,they will share the charge equally,so each capacitor now has a charge $Q' = \frac{Q}{2}$.The new potential difference across each capacitor is $V' = \frac{Q'}{C} = \frac{Q}{2C} = \frac{V}{2}$.The energy stored in each capacitor is $U' = \frac{1}{2} C(V')^2 = \frac{1}{2} C \left(\frac{V}{2}\right)^2 = \frac{1}{2} C \frac{V^2}{4} = \frac{1}{4} \left(\frac{1}{2} CV^2\right) = \frac{U}{4}$.

$A$ capacitor is charged with a battery and the energy stored is $U$. After disconnecting the battery,another capacitor of the same capacity is connected in parallel to the first capacitor. Then the energy stored in each capacitor is

Similar Questions

Two charged spheres of radii $a$ and $b$ are connected by a wire. The ratio of the electric fields on their surfaces $E_a/E_b$ is:

$A$ $20 \mu F$ capacitor is charged to $5 V$ and isolated. It is then connected in parallel with an uncharged $30 \mu F$ capacitor. The decrease in the energy of the system will be (in $\text{J}$)

Two metal spheres of radii $0.01 \ m$ and $0.02 \ m$ are given a charge of $15 \ mC$ and $45 \ mC$ respectively. They are then connected by a wire. The final charge on the first sphere is $\ldots \ldots \ldots \times 10^{-3} \ C$.

Energy of a charged capacitor is $U$. Now it is removed from a battery and then connected to two other identical uncharged capacitors in parallel. What will be the energy of each capacitor?

Two capacitors of $2\ \mu F$ and $3\ \mu F$ are charged to $300\ V$ and $500\ V$ respectively. When they are connected in parallel, the energy lost is: (in $J$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module