(D) From the graph,the potential difference $V$ as a function of time $t$ is a linear equation: $V(t) = mt + c$.At $t=0$,$V=2\, V$,so the intercept $c

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(D) From the graph,the potential difference $V$ as a function of time $t$ is a linear equation: $V(t) = mt + c$.At $t=0$,$V=2\, V$,so the intercept $c=2$.At $t=3\, s$,$V=8\, V$,so the slope $m = \frac{8-2}{3-0} = \frac{6}{3} = 2\, V/s$.Thus,$V(t) = 2t + 2$.For a capacitor,$V = \frac{q}{C} = \frac{1}{C} \int i \, dt$.Given $i = 1\, A$,we have $V = \frac{1}{C} \int 1 \, dt = \frac{t}{C} + V_0$,where $V_0$ is the initial voltage at $t=0$.Comparing $V(t) = \frac{1}{C}t + 2$ with $V(t) = 2t + 2$,we get $\frac{1}{C} = 2$,which implies $C = 0.5\, F$.

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

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$A$ circuit element is placed in a closed box. At time $t=0$,a constant current generator supplying a current of $1\, A$ is connected across the box. The potential difference across the box varies according to the graph shown in the figure. The element in the box is:

A
resistance of $2\, \Omega$
B
battery of $emf\, 6\, V$
C
inductance of $2\, H$
D
capacitance of $0.5\, F$

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Electric Potential and Capacitance

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Charging and Discharging of Capacitance and RC circuit (DC)

Find the time constant for the given circuit.

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The charge on the capacitor of capacitance $C$ shown in the figure below will be

MediumWBJEE 2011

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$A$ charged capacitor is allowed to discharge through a resistance of $2 \, \Omega$ by closing the switch $S$ at the instant $t = 0$. At time $t = \ln 2 \, \mu s$,the reading of the ammeter falls to half of its initial value. The resistance of the ammeter is equal to:

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The circuit shown in the figure consists of a charged capacitor of capacity $3\, \mu F$ and a charge of $30\, \mu C$. At time $t = 0,$ when the key is closed,the value of current flowing through the $5\, M\Omega$ resistor is $'x'\, \mu A$. The value of $'x'$ to the nearest integer is .........

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Two identical capacitors $A$ and $B$,charged to the same potential $V$,are connected in two different circuits as shown below at time $t=0$. If the charge on capacitors $A$ and $B$ at time $t=CR$ is $Q_{A}$ and $Q_{B}$ respectively,then (Here $e$ is the base of natural logarithm):

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$A$ circuit element is placed in a closed box. At time $t=0$,a constant current generator supplying a current of $1\, A$ is connected across the box. The potential difference across the box varies according to the graph shown in the figure. The element in the box is:

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Find the time constant for the given circuit.

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$A$ charged capacitor is allowed to discharge through a resistance of $2 \, \Omega$ by closing the switch $S$ at the instant $t = 0$. At time $t = \ln 2 \, \mu s$,the reading of the ammeter falls to half of its initial value. The resistance of the ammeter is equal to:

The circuit shown in the figure consists of a charged capacitor of capacity $3\, \mu F$ and a charge of $30\, \mu C$. At time $t = 0,$ when the key is closed,the value of current flowing through the $5\, M\Omega$ resistor is $'x'\, \mu A$. The value of $'x'$ to the nearest integer is .........

Two identical capacitors $A$ and $B$,charged to the same potential $V$,are connected in two different circuits as shown below at time $t=0$. If the charge on capacitors $A$ and $B$ at time $t=CR$ is $Q_{A}$ and $Q_{B}$ respectively,then (Here $e$ is the base of natural logarithm):

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