A capacitor of capacitance $900\,\mu F$ is charged by a $100\,V$ battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as $x \times 10^{-2}\,J$. The value of $x$ is $..............$
A capacitor of capacitance $900\,\mu F$ is charged by a $100\,V$ battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as $x \times 10^{-2}\,J$. The value of $x$ is $..............$
- [JEE MAIN 2023]
- A
$224$
- B
$223$
- C
$222$
- D
$225$
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Consider a simple $RC$ circuit as shown in Figure $1$.
Process $1$: In the circuit the switch $S$ is closed at $t=0$ and the capacitor is fully charged to voltage $V_0$ (i.e. charging continues for time $T \gg R C$ ). In the process some dissipation ( $E_D$ ) occurs across the resistance $R$. The amount of energy finally stored in the fully charged capacitor is $EC$.
Process $2$: In a different process the voltage is first set to $\frac{V_0}{3}$ and maintained for a charging time $T \gg R C$. Then the voltage is raised to $\frac{2 \mathrm{~V}_0}{3}$ without discharging the capacitor and again maintained for time $\mathrm{T} \gg \mathrm{RC}$. The process is repeated one more time by raising the voltage to $V_0$ and the capacitor is charged to the same final
take $\mathrm{V}_0$ as voltage
These two processes are depicted in Figure $2$.
($1$) In Process $1$, the energy stored in the capacitor $E_C$ and heat dissipated across resistance $E_D$ are released by:
$[A]$ $E_C=E_D$ $[B]$ $E_C=E_D \ln 2$ $[C]$ $\mathrm{E}_{\mathrm{C}}=\frac{1}{2} \mathrm{E}_{\mathrm{D}}$ $[D]$ $E_C=2 E_D$
($2$) In Process $2$, total energy dissipated across the resistance $E_D$ is:
$[A]$ $\mathrm{E}_{\mathrm{D}}=\frac{1}{2} \mathrm{CV}_0^2$ $[B]$ $\mathrm{E}_{\mathrm{D}}=3\left(\frac{1}{2} \mathrm{CV}_0^2\right)$ $[C]$ $\mathrm{E}_{\mathrm{D}}=\frac{1}{3}\left(\frac{1}{2} \mathrm{CV}_0^2\right)$ $[D]$ $\mathrm{E}_{\mathrm{D}}=3 \mathrm{CV}_0^2$
Given the answer quetion ($1$) and ($2$)
Consider a simple $RC$ circuit as shown in Figure $1$.
Process $1$: In the circuit the switch $S$ is closed at $t=0$ and the capacitor is fully charged to voltage $V_0$ (i.e. charging continues for time $T \gg R C$ ). In the process some dissipation ( $E_D$ ) occurs across the resistance $R$. The amount of energy finally stored in the fully charged capacitor is $EC$.
Process $2$: In a different process the voltage is first set to $\frac{V_0}{3}$ and maintained for a charging time $T \gg R C$. Then the voltage is raised to $\frac{2 \mathrm{~V}_0}{3}$ without discharging the capacitor and again maintained for time $\mathrm{T} \gg \mathrm{RC}$. The process is repeated one more time by raising the voltage to $V_0$ and the capacitor is charged to the same final
take $\mathrm{V}_0$ as voltage
These two processes are depicted in Figure $2$.
($1$) In Process $1$, the energy stored in the capacitor $E_C$ and heat dissipated across resistance $E_D$ are released by:
$[A]$ $E_C=E_D$ $[B]$ $E_C=E_D \ln 2$ $[C]$ $\mathrm{E}_{\mathrm{C}}=\frac{1}{2} \mathrm{E}_{\mathrm{D}}$ $[D]$ $E_C=2 E_D$
($2$) In Process $2$, total energy dissipated across the resistance $E_D$ is:
$[A]$ $\mathrm{E}_{\mathrm{D}}=\frac{1}{2} \mathrm{CV}_0^2$ $[B]$ $\mathrm{E}_{\mathrm{D}}=3\left(\frac{1}{2} \mathrm{CV}_0^2\right)$ $[C]$ $\mathrm{E}_{\mathrm{D}}=\frac{1}{3}\left(\frac{1}{2} \mathrm{CV}_0^2\right)$ $[D]$ $\mathrm{E}_{\mathrm{D}}=3 \mathrm{CV}_0^2$
Given the answer quetion ($1$) and ($2$)
- [IIT 2017]
A series combination of $n_1$ capacitors, each of value $C_1$ is charged by a source of potential difference $4\, V.$ When another parallel combination of $n_2$ capacitors, each of value $C_2,$ is charged by a source of potential difference $V$, it has the same (total) energy stored in it, as the first combination has. The value of $C_2,$ in terms of $C_1$ is then
A series combination of $n_1$ capacitors, each of value $C_1$ is charged by a source of potential difference $4\, V.$ When another parallel combination of $n_2$ capacitors, each of value $C_2,$ is charged by a source of potential difference $V$, it has the same (total) energy stored in it, as the first combination has. The value of $C_2,$ in terms of $C_1$ is then
- [AIEEE 2012]