(B) The displacement current $i_d$ in a capacitor is equal to the conduction current $i_c$ in the connecting wires.The formula for current is $i = \fr

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(B) The displacement current $i_d$ in a capacitor is equal to the conduction current $i_c$ in the connecting wires.The formula for current is $i = \frac{dq}{dt}$.Since $q = CV$,we have $i_d = \frac{d}{dt}(CV)$.Given that the capacitance $C$ is constant,$i_d = C \frac{dV}{dt}$.Substituting the given values: $C = 2\,\mu F = 2 \times 10^{-6}\, F$ and $\frac{dV}{dt} = 10^6\, V/s$.$i_d = (2 \times 10^{-6}\, F) \times (10^6\, V/s) = 2\, A$.

Class 12 Physics Electrostatic Potential and Capacitance Charging and Discharging of Capacitance and RC circuit (DC)

Medium

The potential difference between the plates of a parallel plate capacitor is changing at the rate of $10^6\, V/s$. If the capacitance is $2\,\mu F$,the displacement current in the dielectric of the capacitor will be......$A$

A
$1$
B
$2$
C
$3$
D
$4$

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Electrostatic Potential and Capacitance

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Charging and Discharging of Capacitance and RC circuit (DC)

The following circuit consists of a $5 \,\mu F$ capacitor,having a charge of $50 \,\mu C$ as shown. The switch is closed at $t=0$. The value of the current in the $2 \,M \Omega$ resistor at $t=0$ is ........... $\mu A$.

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In the following circuit,the switch $S$ is closed at $t = 0.$ The charge on the capacitor $C_1$ as a function of time will be given by $\left( {{C_{eq}} = \frac{{{C_1}{C_2}}}{{{C_1} + {C_2}}}} \right).$

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The capacitor shown in the figure is in a steady state. The energy stored in the capacitor is

Medium

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What are the charges stored in the $1 \mu F$ and $2 \mu F$ capacitors in the circuit as shown in the figure once the current $(I)$ becomes steady?

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Given $R_1 = 1\,\Omega$,$C_1 = 2\,\mu F$ and $R_2 = 2\,\Omega$,$C_2 = 4\,\mu F$. The time constants (in $\mu s$) for the circuits $I, II, III$ are respectively:

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The potential difference between the plates of a parallel plate capacitor is changing at the rate of $10^6\, V/s$. If the capacitance is $2\,\mu F$,the displacement current in the dielectric of the capacitor will be......$A$

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The following circuit consists of a $5 \,\mu F$ capacitor,having a charge of $50 \,\mu C$ as shown. The switch is closed at $t=0$. The value of the current in the $2 \,M \Omega$ resistor at $t=0$ is ........... $\mu A$.

In the following circuit,the switch $S$ is closed at $t = 0.$ The charge on the capacitor $C_1$ as a function of time will be given by $\left( {{C_{eq}} = \frac{{{C_1}{C_2}}}{{{C_1} + {C_2}}}} \right).$

The capacitor shown in the figure is in a steady state. The energy stored in the capacitor is

What are the charges stored in the $1 \mu F$ and $2 \mu F$ capacitors in the circuit as shown in the figure once the current $(I)$ becomes steady?

Given $R_1 = 1\,\Omega$,$C_1 = 2\,\mu F$ and $R_2 = 2\,\Omega$,$C_2 = 4\,\mu F$. The time constants (in $\mu s$) for the circuits $I, II, III$ are respectively:

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