A parallel plate capacitor of capacity 100 mu | vedclass

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

Question

(B) Initial capacitance $C = 100 \mu F = 100 	imes 10^{-6} 	ext{ F}$ and potential $V = 50 	ext{ V}$.Initial energy stored $E_1 = \frac{1}{2} C V^2

Vedclass · Accepted Answer

$125 	imes 10^{-3}$

Vedclass · Answer

(B) Initial capacitance $C = 100 \mu F = 100 	imes 10^{-6} 	ext{ F}$ and potential $V = 50 	ext{ V}$.Initial energy stored $E_1 = \frac{1}{2} C V^2 = \frac{1}{2} 	imes 100 	imes 10^{-6} 	imes (50)^2 = 50 	imes 10^{-6} 	imes 2500 = 0.125 	ext{ J} = 125 	imes 10^{-3} 	ext{ J}$.When the distance $d$ is doubled,the new capacitance $C' = \frac{\epsilon_0 A}{2d} = \frac{C}{2} = 50 \mu F$.Since the battery remains connected,the potential $V$ remains $50 	ext{ V}$.Final energy stored $E_2 = \frac{1}{2} C' V^2 = \frac{1}{2} 	imes 50 	imes 10^{-6} 	imes (50)^2 = 25 	imes 10^{-6} 	imes 2500 = 0.0625 	ext{ J} = 62.5 	imes 10^{-3} 	ext{ J}$.Charge on the capacitor initially $Q_1 = CV = 100 	imes 10^{-6} 	imes 50 = 5 	imes 10^{-3} 	ext{ C}$.Charge on the capacitor finally $Q_2 = C'V = 50 	imes 10^{-6} 	imes 50 = 2.5 	imes 10^{-3} 	ext{ C}$.Change in charge $\Delta Q = Q_2 - Q_1 = -2.5 	imes 10^{-3} 	ext{ C}$.Work done by the battery $W = \Delta Q 	imes V = (-2.5 	imes 10^{-3}) 	imes 50 = -125 	imes 10^{-3} 	ext{ J}$.The negative sign indicates that energy is returned to the battery. The magnitude of energy change is $125 	imes 10^{-3} 	ext{ J}$.

Similar Questions

$100$ capacitors,each having a capacity of $10\,\mu F$,are connected in parallel and are charged by a potential difference of $100\,kV$. The energy stored in the capacitors and the cost of charging them,if electrical energy costs $108\;paise\;per\;kWh$,will be

The figure shows a diagonal symmetric arrangement of capacitors and a battery. The potentials of the points $B$ and $D$ are:

Three capacitors are connected to a battery as shown in the figure. The ratio of charge on capacitors $C_3$ and $C_1$ is (in $.5$)

In the given circuit,$C_1=2\,\mu F, C_2=0.2\,\mu F, C_3=2\,\mu F, C_4=4\,\mu F, C_5=2\,\mu F, C_6=2\,\mu F$. The charge stored on capacitor $C_4$ is $.....\mu C$.

When a potential difference of $10^{3} \, V$ is applied between $A$ and $B$, a charge of $0.75 \, mC$ is stored in the circuit. The value of $C$ is (in $\mu F$):

Vedclass Test Series

Exam Paper Generator

Online Exam Module