(A) In an $RC$ series circuit charging from a battery of $EMF$ $V$,the voltage across the capacitor at time $t$ is given by $V_C = V(1 - e^{-t/RC})$.T

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

(A) In an $RC$ series circuit charging from a battery of $EMF$ $V$,the voltage across the capacitor at time $t$ is given by $V_C = V(1 - e^{-t/RC})$.The voltage across the resistor at time $t$ is given by $V_R = V e^{-t/RC}$.Given that $V_C = 7 V_R$,we substitute the expressions:$V(1 - e^{-t/RC}) = 7(V e^{-t/RC})$$1 - e^{-t/RC} = 7 e^{-t/RC}$$1 = 8 e^{-t/RC}$$e^{t/RC} = 8$Taking the natural logarithm on both sides:$t/RC = \ln 8$$t = RC \ln(2^3)$$t = 3 \, RC \ln 2$.

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

Difficult

$A$ resistance $R$ and a capacitance $C$ are connected in series to a battery of negligible internal resistance through a key. The key is closed at $t = 0$. If after $t \, s$ the voltage across the capacitance is seven times the voltage across $R$,the value of $t$ is:

AIEEE 2012 All AIEEE

A
$3 \, RC \ln 2$
B
$2 \, RC \ln 2$
C
$2 \, RC \ln 7$
D
$3 \, RC \ln 7$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Physics Questions

Chapter

Electric Potential and Capacitance

Subtopic

Charging and Discharging of Capacitance and RC circuit (DC)

Previous Year

AIEEE 2012 Paper All AIEEE years →

$A$ capacitor of capacitance $C$ is discharging through a resistor $R$. Let $t_1$ be the time taken for the energy stored in the capacitor to reduce to half of its initial value,and $t_2$ be the time taken for the charge to reduce to one-fourth of its initial value. Then the ratio $t_1 / t_2$ is:

Difficult

View Solution

$A$ filter circuit used in a rectifier has a load resistance of $200 \Omega$ and a capacitance of $15 \mu\text{F}$. The value of the time constant is . . . . . . .

MediumGUJCET 2025

View Solution

Two identical capacitors $A$ and $B$ are charged to the same potential $V$ and are connected in two circuits at $t = 0,$ as shown in the figure. The charge on the capacitors at time $t = CR$ are respectively:

Medium

View Solution

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?

MediumWBJEE 2025

View Solution

How much time does it take for the current to decay to half of its initial value in the following charging circuit?

Difficult

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ resistance $R$ and a capacitance $C$ are connected in series to a battery of negligible internal resistance through a key. The key is closed at $t = 0$. If after $t \, s$ the voltage across the capacitance is seven times the voltage across $R$,the value of $t$ is:

Similar Questions

$A$ capacitor of capacitance $C$ is discharging through a resistor $R$. Let $t_1$ be the time taken for the energy stored in the capacitor to reduce to half of its initial value,and $t_2$ be the time taken for the charge to reduce to one-fourth of its initial value. Then the ratio $t_1 / t_2$ is:

$A$ filter circuit used in a rectifier has a load resistance of $200 \Omega$ and a capacitance of $15 \mu\text{F}$. The value of the time constant is . . . . . . .

Two identical capacitors $A$ and $B$ are charged to the same potential $V$ and are connected in two circuits at $t = 0,$ as shown in the figure. The charge on the capacitors at time $t = CR$ are respectively:

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?

How much time does it take for the current to decay to half of its initial value in the following charging circuit?

Vedclass Test Series

Exam Paper Generator

Online Exam Module