A parallel plate capacitor with plate separation d is connected to a battery. Th

Question

A parallel plate capacitor with plate separation d is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V. (C is the capacitance and U is the stored energy.) Answer the following questions regarding the capacitor charged by a battery. For each statement below, select True or False.

True False  After being disconnected from the battery, increasing d increases V.
True False  After being disconnected from the battery, inserting a dielectric with will decrease V.
True False  With the capacitor connected to the battery, decreasing d increases C.
True False  After being disconnected from the battery, inserting a dielectric with will increase C.
True False  After being disconnected from the battery, inserting a dielectric with will decrease U.
True False  After being disconnected from the battery, decreasing d increases U.

Explanation / Answer

Formula Used:

1. Q = CV, 2. C =e0*A/d 3. e0 = k*er   4. U = 0.5*C*V^2

A. TRUE.

Reason:   Now if we increase d it will decrease C by formula 2, and if C decrease then V increases by formula 1

B. FALSE

Reason: Inserting a dielctric will increase C as C is proportional to dielectric constant by formula 3, and if C increase then V decreases by formula 1.

C. TRUE

The Voltage is constant since battery is connected so decreasing d will increase C by formula 2.

D. TRUE

Inserting a dielctric will increase C as C is proportional to dielectric constant by formula 3.

E. FALSE

Inserting a dielectric will increase C and Cis proportional to U so U will increase if C increases by formula 4.

F. TRUE

Decreasong d will increase C by formula 2, and increasing C will increase U by formula 4.

Comment Below if you have any doubt.

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