Question:

A parallel plate capacitor is connected to a battery as shown in figure. Consider two situations
(i) key $K$ is kept closed and plates of capacitors are moved apart using insulating handle (ii) key $K$ is opened and plates of capacitors are moved apart using insulating handle Which of the following statements is correct?

Updated On: Jun 23, 2023
  • In (i), $Q$ remains same but $C$ changes
  • In (ii) $V$ remains same but $C$ changes
  • In (i) $V$ remains same and hence $Q$ changes.
  • In $(ii)$ both $Q$ and $V$ changes
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The Correct Option is C

Solution and Explanation

When key K is kept closed, condenser C is charged to potential V. When plates of capacitors are moved apart, its capacitance, C = $\frac {\epsilon_o A}{d}$ decreases. As potential of condenser remains same, charge $Q = CV$ decreases.So option is correct. Once key $K$ is closed, condenser gets charged, $Q = CV$ . Now, if key K is opened, battery is disconnected, no more charging can occur i.e. Q remains same. As plates or capacitor are moved apart, its capacity $C = \frac {epsilon_o A}{d}$ decreases. Therefore, its potential , $V =\frac {q}{C} increases$
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Concepts Used:

Electrostatic Potential and Capacitance

Electrostatic Potential

The potential of a point is defined as the work done per unit charge that results in bringing a charge from infinity to a certain point.

Some major things that we should know about electric potential:

  • They are denoted by V and are a scalar quantity.
  • It is measured in volts.

Capacitance

The ability of a capacitor of holding the energy in form of an electric charge is defined as capacitance. Similarly, we can also say that capacitance is the storing ability of capacitors, and the unit in which they are measured is “farads”.

Read More: Electrostatic Potential and Capacitance

The capacitor is in Series and in Parallel as defined below;

In Series

Both the Capacitors C1 and C2 can easily get connected in series. When the capacitors are connected in series then the total capacitance that is Ctotal is less than any one of the capacitor’s capacitance.

In Parallel

Both Capacitor C1 and C2 are connected in parallel. When the capacitors are connected parallelly then the total capacitance that is Ctotal is any one of the capacitor’s capacitance.