A capacitor of capacity C_1 is charged to a p | vedclass

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

Question

(A) The initial energy stored in the capacitor $C_1$ is given by:$U_1 = \frac{1}{2} C_1 V_0^2$When the switch $S$ is closed,the charge $Q = C_1 V_0$ i

Vedclass · Accepted Answer

$\frac{C_1 + C_2}{C_1}$

Vedclass · Answer

(A) The initial energy stored in the capacitor $C_1$ is given by:$U_1 = \frac{1}{2} C_1 V_0^2$When the switch $S$ is closed,the charge $Q = C_1 V_0$ is redistributed between the two capacitors until they reach a common potential $V$. By the principle of conservation of charge:$C_1 V_0 = (C_1 + C_2) V$$V = \frac{C_1 V_0}{C_1 + C_2}$The final energy stored in the system is:$U_2 = \frac{1}{2} (C_1 + C_2) V^2 = \frac{1}{2} (C_1 + C_2) \left( \frac{C_1 V_0}{C_1 + C_2} \right)^2 = \frac{1}{2} \frac{C_1^2 V_0^2}{C_1 + C_2}$The ratio of the energy before and after the connection is:$\frac{U_1}{U_2} = \frac{\frac{1}{2} C_1 V_0^2}{\frac{1}{2} \frac{C_1^2 V_0^2}{C_1 + C_2}} = \frac{C_1 (C_1 + C_2)}{C_1^2} = \frac{C_1 + C_2}{C_1}$

$A$ capacitor of capacity $C_1$ is charged to a potential of $V_0$. After disconnecting it from the battery,it is connected to a neutral capacitor of capacity $C_2$ as shown in the adjoining figure. The ratio of the energy of the system before and after the connection of switch $S$ will be

Similar Questions

$A$ $400\, pF$ capacitor is charged with a $100\, V$ battery. After disconnecting the battery,this capacitor is connected to another uncharged $400\, pF$ capacitor. Find the energy loss.

Two capacitors of $1\,\mu F$ and $2\,\mu F$ are charged to $1200\,V$. If they are connected in parallel such that the positive plate of one is connected to the negative plate of the other,what will be the new charge on each capacitor?

$A$ capacitor of capacitance $C_1 = 1 \ \mu F$ is charged using a $9 \ V$ battery. $C_1$ is then removed from the battery and connected to capacitors $C_2$ and $C_3$ of $2 \ \mu F$ and $3 \ \mu F$ respectively,as shown in the figure. Find the charge on $C_3$ after equilibrium is reached.

Energy $E$ is stored in a parallel plate capacitor $C_1$. An identical uncharged capacitor $C_2$ is connected to it,kept in contact with it for a while,and then disconnected. The energy stored in $C_2$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module