Let C be the capacitance of a capacitor disch | vedclass

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

Question

(D) The energy stored in a capacitor is given by $U = \frac{q^2}{2C}$.For energy to reduce to half its initial value: $\frac{U_0}{2} = \frac{q^2}{2C}

Vedclass · Accepted Answer

$0.25$

Vedclass · Answer

(D) The energy stored in a capacitor is given by $U = \frac{q^2}{2C}$.For energy to reduce to half its initial value: $\frac{U_0}{2} = \frac{q^2}{2C} \Rightarrow \frac{q_0^2}{2} = q^2 \Rightarrow q = \frac{q_0}{\sqrt{2}}$.Using the discharging equation $q = q_0 e^{-t/RC}$,we have $\frac{q_0}{\sqrt{2}} = q_0 e^{-t_1/RC}$.Taking the natural logarithm: $-\frac{t_1}{RC} = \ln(1/\sqrt{2}) = -\frac{1}{2} \ln 2$,so $t_1 = \frac{RC \ln 2}{2}$.For charge to reduce to one-fourth its initial value: $\frac{q_0}{4} = q_0 e^{-t_2/RC}$.Taking the natural logarithm: $-\frac{t_2}{RC} = \ln(1/4) = -2 \ln 2$,so $t_2 = 2RC \ln 2$.The ratio $\frac{t_1}{t_2} = \frac{(RC \ln 2) / 2}{2RC \ln 2} = \frac{1}{4} = 0.25$.

Similar Questions

$A$ capacitor of $8 \mu\text{F}$ is connected as shown in the circuit. Find the charge on the plates of the capacitor. (in $\mu\text{C}$)

$A$ capacitor is connected to a $20\, V$ battery through a resistance of $10\, \Omega$. It is found that the potential difference across the capacitor rises to $2\, V$ in $1\, \mu s$. The capacitance of the capacitor is $....\, \mu F$. Given: $\ln(10/9) = 0.105$.

The capacitor shown in the figure is in a steady state. The energy stored in the capacitor is

The electric field between the two parallel plates of a capacitor of $1.5 \mu F$ capacitance drops to one third of its initial value in $6.6 \mu s$ when the plates are connected by a thin wire. The resistance of this wire is . . . . . . . $\Omega$. (Given,$\log_{e} 3 = 1.1$)

As shown in the figure,if a capacitor of capacitance $C$ is charged by connecting it with a resistance $R$ and a battery of $EMF$ $V$,then the total energy supplied by the battery is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module