In which of the following cases is the stored | vedclass

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

Question

(B) The energy stored in a capacitor is given by $U = \frac{q^2}{2C}$. To maximize the energy $U$,we need to minimize the capacitance $C$ for a given

Vedclass · Accepted Answer

Vedclass · Answer

(B) The energy stored in a capacitor is given by $U = \frac{q^2}{2C}$. To maximize the energy $U$,we need to minimize the capacitance $C$ for a given charge $q$.For a spherical capacitor with inner radius $a$ and outer radius $b$,the capacitance is $C = \frac{4\pi \epsilon_0 ab}{b-a}$.In case $B$,the outer sphere is grounded,forming a standard spherical capacitor with $C_B = \frac{4\pi \epsilon_0 ab}{b-a}$.In case $C$,the inner sphere is grounded,and the charge $q$ is on the outer sphere. The capacitance is $C_C = \frac{4\pi \epsilon_0 b^2}{b-a}$.Comparing the two,$C_C > C_B$ because $b > a$. Since $U = \frac{q^2}{2C}$,a smaller capacitance results in a larger stored energy.Therefore,the configuration with the smallest capacitance (Case $B$) will store the maximum energy for a given charge $q$ on the inner sphere.

In which of the following cases is the stored energy maximum?

Similar Questions

Four capacitors with capacitances $C_1 = 1\,\mu F, C_2 = 1.5\,\mu F, C_3 = 2.5\,\mu F$ and $C_4 = 0.5\,\mu F$ are connected as shown and are connected to a $30\,V$ source. The potential difference between points $a$ and $b$ is.....$V$.

$A$ capacitor of $2\,\mu F$ capacitance is charged steadily from $0$ to $5\,C$. Which of the following graphs correctly represents the variation of potential difference across its plates with respect to the charge on the capacitor?

Find the ratio $\frac{C_{DE}}{C_{AB}}$ for the given circuit.

$A$ proton and a deuteron are initially at rest and are accelerated through the same potential difference. Which of the following is false concerning the final properties of the two particles?

Vedclass Test Series

Exam Paper Generator

Online Exam Module