A 4 mu F capacitor and a resistance of 2.5 , | vedclass

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

Question

(A) The potential difference across the capacitor is $V_C = V_0(1 - e^{-t/RC})$ and across the resistor is $V_R = V_0 e^{-t/RC}$.Given that $V_C = 3 V

Vedclass · Accepted Answer

$13.86$

Vedclass · Answer

(A) The potential difference across the capacitor is $V_C = V_0(1 - e^{-t/RC})$ and across the resistor is $V_R = V_0 e^{-t/RC}$.Given that $V_C = 3 V_R$,we have $V_0(1 - e^{-t/RC}) = 3 V_0 e^{-t/RC}$.Dividing by $V_0$,we get $1 - e^{-t/RC} = 3 e^{-t/RC}$,which simplifies to $1 = 4 e^{-t/RC}$.Thus,$e^{t/RC} = 4$,or $t/RC = \ln(4) = 2 \ln(2)$.Given $R = 2.5 	imes 10^6 \, \Omega$ and $C = 4 	imes 10^{-6} \, F$,the time constant $	au = RC = (2.5 	imes 10^6) 	imes (4 	imes 10^{-6}) = 10 \, s$.Substituting the values,$t = 10 	imes 2 	imes 0.693 = 13.86 \, s$.

$A$ $4 \mu F$ capacitor and a resistance of $2.5 \, M\Omega$ are in series with a $12 \, V$ battery. Find the time after which the potential difference across the capacitor is $3$ times the potential difference across the resistor. (Given $\ln(2) = 0.693$)

Similar Questions

$A$ capacitor of capacitance $C = 1 \, \mu F$ is suddenly connected to a battery of $100 \, V$ through a resistance $R = 100 \, \Omega$. The time taken for the capacitor to be charged to $50 \, V$ is $.... \times 10^{-4} \, s$. (Take $\ln 2 = 0.69$)

An electric bulb, a capacitor, a battery, and a switch are all connected in series in a circuit. How does the intensity of light vary when the switch is turned on?

In the given circuit,switch $S$ is closed at $t = 0$. The current $I$ in the figure at time $t$ is

At $t = 0$,switch $S$ is closed. The charge on the capacitor is varying with time $t$ as $Q = Q_0(1 - e^{-\alpha t})$. Find the value of $Q_0$.

The figure shows an experimental graph of the discharging of a capacitor in an $RC$ circuit. The time constant of this circuit lies between which of the following time intervals?

Vedclass Test Series

Exam Paper Generator

Online Exam Module