Parallel-plate capacitor: battery connected or disconnected (changing d and inserting a dielectric)

Pull the plates apart or push in a dielectric with the battery still connected (V stays the same) and with the battery removed (Q stays the same). See what happens to C, Q, V, E, the energy and the force between the plates.

Also searched as: capacitor with battery connected and disconnected · capacitor with battery connected and disconnected · capacitor dielectric inserted battery connected · parallel plate capacitor distance changed · energy stored in a capacitor · capacitor constant charge constant potential

About this experiment

Aim

To see how the capacitance, charge, potential difference, field and stored energy of a parallel-plate capacitor change when the distance between the plates is changed or a dielectric is inserted, with the battery connected and with the battery removed.

Theory

A parallel-plate capacitor has C = K ε₀ A / d. Making d larger lowers C, putting in a dielectric of constant K raises C by the factor K. The charge Q, voltage V and capacitance are related by Q = C V and the energy stored is U = ½ C V² = Q²/2C.

Battery connected: the battery keeps V constant. If C changes, charge flows to or from the battery so that Q = C V changes. The field E = V/d changes as 1/d. The energy U = ½ C V² is proportional to C: it falls when the plates are pulled apart, because charge flows back into the battery, and it rises when a dielectric is inserted.

Battery disconnected: the charge Q is trapped on the plates and stays constant. If C changes, V = Q/C changes. The field E = Q/(K ε₀ A) does not depend on d (without dielectric). The energy U = Q²/2C is proportional to 1/C: it rises when the plates are pulled apart. The extra energy is the work done against the attraction between the plates. When a dielectric is pushed in, C increases, V falls and the stored energy decreases: the slab is pulled in.

Formulas used

• C = K ε₀ A / d, Q = C V
• U = ½ C V² = ½ Q V = Q² / 2C
• E = V / d = Q / (K ε₀ A)
• force between the plates F = ½ Q E
• battery connected: V fixed; disconnected: Q fixed

Procedure: what to do in the virtual lab

1. Charge it with 12 V at d = 3 mm. With the battery connected increase d to 6 mm and note C, Q, V and U.
2. Do the same with the battery disconnected and compare the changes. Which quantity is constant in each case?
3. Insert a dielectric (K = 5): compare the two cases again.
4. Use the graph: why do the two curves go in opposite directions?
5. Find the force between the plates and see how it changes with d in both cases.

Observations to make

• Connected: V constant; Q, C and U fall as d increases. Disconnected: Q constant; V and U rise as d increases.
• A dielectric always increases C; with the battery removed it lowers V and U.
• The field with fixed Q does not change when d changes.

What you can change in this experiment

• Battery: connected (the potential difference V stays constant) / disconnected after charging (the charge Q stays constant)
• Battery voltage when it charged the capacitor (1 to 24 V)
• Area of each plate (50 to 400 cm²)
• Distance between the plates now (1 to 10 mm)
• Dielectric constant of the slab filling the gap (1 = air)

Viva questions on Parallel-plate capacitor

Questions an examiner may ask in the Class 12 physics practical. Run the experiment in the lab to find the answers yourself, then check them in the Learn tab.

1. What is the effect on the energy when the plates of an isolated charged capacitor are pulled apart?
2. What stays constant when the battery stays connected?
3. What is the effect of a dielectric on C, Q, V and U?
4. What is the force between the plates of a capacitor?

Frequently asked questions

Syllabus: Class XII Physics, Chapter 2 — Electrostatic Potential and Capacitance, §2.8 (capacitors), §2.9 (dielectrics), §2.12 (energy stored)

What you do in the lab

Change the controls and watch the physics behave in real time in 3D. Live readouts and graphs show the numbers behind it, and the Learn tab has the theory, procedure, observations and viva questions. Works on a phone or a laptop, in English and Hindi.

Topics: capacitance · capacitor with battery · dielectric · energy stored in a capacitor · constant charge · constant potential · electrostatic potential and capacitance

Read the full guide: Capacitance.

More from this chapter

• Connecting two capacitors: charge sharing and energy loss
• Capacitors in series/parallel, charging energy
• Capacitor with a dielectric slab
• Equipotential surfaces and potential energy
• Parallel plate capacitor with dielectric
• Van de Graaff generator

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