A charged capacitor is allowed to discharge t | vedclass

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

Question

(A) The current in a discharging $RC$ circuit is given by $I(t) = I_0 e^{-t/	au}$,where $	au = R_{eq}C$ is the time constant.Here,$R_{eq} = R + r$,w

Vedclass · Accepted Answer

$0 \, \Omega$

Vedclass · Answer

(A) The current in a discharging $RC$ circuit is given by $I(t) = I_0 e^{-t/	au}$,where $	au = R_{eq}C$ is the time constant.Here,$R_{eq} = R + r$,where $R = 2 \, \Omega$ is the external resistance and $r$ is the resistance of the ammeter.The capacitance is $C = 0.5 \, \mu F = 0.5 	imes 10^{-6} \, F$.Given that at $t = \ln 2 \, \mu s = \ln 2 	imes 10^{-6} \, s$,the current $I(t) = I_0 / 2$.Substituting these values into the equation: $I_0 / 2 = I_0 e^{-t/	au} \Rightarrow 1/2 = e^{-t/	au}$.Taking the natural logarithm on both sides: $\ln(1/2) = -t/	au \Rightarrow -\ln 2 = -t/	au \Rightarrow 	au = t / \ln 2$.Substituting $t = \ln 2 \, \mu s$: $	au = (\ln 2 \, \mu s) / \ln 2 = 1 \, \mu s = 10^{-6} \, s$.Since $	au = (R + r)C$,we have $10^{-6} = (2 + r) 	imes 0.5 	imes 10^{-6}$.Dividing both sides by $10^{-6}$: $1 = (2 + r) 	imes 0.5$.$2 = 2 + r \Rightarrow r = 0 \, \Omega$.

$A$ 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:

Similar Questions

$A$ 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:

The circuit shown has been connected for a long time. The voltage across the capacitor is ............. $V$.

Three identical capacitors are given a charge $Q$ each and they are then allowed to discharge through resistances $R_1, R_2,$ and $R_3$. Their charges,as a function of time,are shown in the graph below. The smallest of the three resistances is

$A$ capacitor is discharging through a resistor $R$. Consider in time $t_{1}$,the energy stored in the capacitor reduces to half of its initial value and in time $t_{2}$,the charge stored reduces to one-eighth of its initial value. The ratio $t_{1} / t_{2}$ will be ................

The circuit shown here has two batteries of $8.0 \, V$ and $16.0 \, V$,three resistors of $3 \, \Omega$,$9 \, \Omega$,and $9 \, \Omega$,and a capacitor of $5.0 \, \mu F$. How much is the current $I$ in the circuit in steady state? ................... $A$

Vedclass Test Series

Exam Paper Generator

Online Exam Module