Capacitor Energy Storage and Supply – Rankers Physics

Parallel Plate Capacitor: Practice Problem & Solution

A capacitor of capacitance C is connected across a battery of potential difference V. Assertion (A): The energy stored in capacitor is \( \frac{1}{2} CV^2 \). Reason (R): The energy supplied by the battery is \( CV^2 \).  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Parallel Plate Capacitor. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A) is true: energy stored in a capacitor is \( U = \frac{1}{2} CV^2 \). Reason (R) is true: the total work done by the battery (energy supplied) is \( W = CV^2 \). However, (R) is not the correct explanation for (A), as half of the supplied energy is dissipated as heat.

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Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. The plates S and T of an uncharged parallel plate capacitor are connected across a battery. The battery is then disconnected and the charged plates are now connected in a system as shown in the figure. The system shown is in equilibrium. All the strings are insulating and massless. The magnitude of charge on one of the capacitor plates is: [Area of plates = A]
2. Assertion (A): It is not possible to make a spherical conductor of capacitor one farad. Reason (R): It is possible for earth as its radius is \( 6400 \text{ km} \).  
3. Two capacitors \( C_1 \) and \( C_2 \) are charged to \( 120\text{V} \) and \( 200\text{V} \) respectively. It is found that by connecting them together the potential on each one can be made zero. Then :
4. Assertion (A): Circuits containing high capacity capacitors, charged to high voltage should be handled with caution, even when the current in the circuit is switched off. Reason (R): When an isolated capacitor is touched by hand or any other part of the human body, there is an easy path to the ground available for the discharge of the capacitor.  
5. A parallel plate capacitor has plates of area A and separation d and is charged to a potential difference V. The charging battery is then disconnected and the plates are pulled apart until their separation is 2d. What is the work required to separated the plates?