A parallel-plate capacitor with adjustable plate separation d and adjustable are

Question

A parallel-plate capacitor with adjustable plate separation d and adjustable area A is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V volts. C is the capacitance and U is the stored energy. Select all that are true: With the capacitor connected to the battery, decreasing d increases U. With the capacitor connected to the battery, increasing the area A will decrease Q. With the capacitor connected to the battery, increasing the area A will increase C. With the capacitor connected to the battery, increasing d decreases Q. With the capacitor connected to the battery, increasing the area A will decrease U. After being disconnected from the battery, decreasing d increases C.

Explanation / Answer

(1)

capacitance: C = e0A/d,   

charge Q = CV = [e0A/d]*V ,

and

energy = U = (1/2)CV^2 = (1/2) [e0A/d]*V^2

From above relation, energy U is inversely proportional to d.

So, energy U increases when d decreasing.

statement 1: true

2.)

charge Q is directly proportional to area A.

the charge increases when the area increases.

statement 2: false

3)

Capacitance C is directly proportional to area A.

the capacitance increases when the area increases.

statement 3: true

4)

charge Q isinversely proportional to distance d.

charge Q decreases when distance increases.

statement 4: true

5)

energy U is directly proportional to area A.

the energy increases when the area increases.

statement 5: false

6)

capacitance C isinversely proportional to distance d.

Capacitance C increases when distance dicreases.

statement 6: true

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