Question

Suppose two parallel-plate capacitors have the same charge Q, but the area of capacitor 1 is A and the area of capacitor 2 is 2 A.If the spacing between the plates, d, is the same in both capacitors, and the voltage across capacitor 1 is V, what is the voltage across capacitor 2?Express your answer in terms of V but do not type in the symbol "V"

Answer 1

V' = V/2

Step-by-step explanation:

The voltage across a parallel plate capacitor is given as follows:

V = Q/C

where,

V = Voltage across capacitor

Q = Charge on Capacitor

C = Capacitance of Capacitor = A∈₀/d

Therefore,

V = Qd/A∈₀

where,

A = Area of plate

d = distance between plates

∈₀ = permittivity of free space

FOR CAPACITOR 1:

Q = Q

d = d

A = A

V = V

Therefore,

V = Qd/A∈₀ --------------- equation (1)

FOR CAPACITOR 2:

V' = ?

Q' = Q

d' = d

A' = 2A

Therefore,

V' = Q'd'/A'∈₀

V' = Qd/2A∈₀

V' = (1/2)(Qd/A∈₀)

using equation (1):

V' = V/2