(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)

When the key $K$ is pressed at time $t = 0$, which of the following statements about the current $I$ in the resistor $AB$ of the given circuit is true?

MediumAIPMT 1995

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$A$ capacitor of capacity $0.1 \mu F$ connected in series to a resistor of $10 M \Omega$ is charged to a certain potential and then made to discharge through the resistor. The time in which the potential will take to fall to half its original value is (Given, $\log _{10} 2=0.3010$ ) (in $\,s$)

DifficultTS EAMCET 2010

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At steady state,the charge on the capacitor,as shown in the circuit below,is . . . . . . $\mu \text{C}.$

MediumJEE MAIN 2025

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Assertion : $A$ capacitor blocks direct current in the steady state.
Reason : The capacitive reactance of the capacitor is inversely proportional to frequency $f$ of the source of $emf$.

EasyAIIMS 2011

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The figure shows an experimental plot for discharging of a capacitor in an $R-C$ circuit. The time constant $\tau$ of this circuit lies between

MediumAIEEE 2012

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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:

Similar Questions

When the key $K$ is pressed at time $t = 0$, which of the following statements about the current $I$ in the resistor $AB$ of the given circuit is true?

$A$ capacitor of capacity $0.1 \mu F$ connected in series to a resistor of $10 M \Omega$ is charged to a certain potential and then made to discharge through the resistor. The time in which the potential will take to fall to half its original value is (Given, $\log _{10} 2=0.3010$ ) (in $\,s$)

At steady state,the charge on the capacitor,as shown in the circuit below,is . . . . . . $\mu \text{C}.$

Assertion : $A$ capacitor blocks direct current in the steady state.Reason : The capacitive reactance of the capacitor is inversely proportional to frequency $f$ of the source of $emf$.

The figure shows an experimental plot for discharging of a capacitor in an $R-C$ circuit. The time constant $\tau$ of this circuit lies between

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Assertion : $A$ capacitor blocks direct current in the steady state.
Reason : The capacitive reactance of the capacitor is inversely proportional to frequency $f$ of the source of $emf$.