Question

Question 2.7: Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. (a) What is the total capacitance of the combination? (b) Determine the charge on each capacitor if the combination is connected to a 100 V supply.

Class 12 - Physics - Electrostatic Potential And Capacitance Electrostatic Potential And Capacitance Page-87

Answer 1

If the capacitors are connected in parallel then equivalent capacitance of capacitors is given by Ceq = C₁ + C₂ + C₃ + .......

Here , C₁ = 2pF, C₂ = 3pF and C₃ = 4pF
so, Ceq = C₁ + C₂ + C₃
Ceq = 2pF + 3pF + 4pF
= 9pF

(b) since the capacitors are in parallel, so the potential difference across each of them is same. e.g., V₁ = V₂ = V₃ = V = 100V
So, charge stored on capacitors are
Q₁ = C₁V = 2pF × 100V = 200pC
Q₂ = C₂V = 3pF × 100V = 300pC
Q₃ = C₃V = 4pF × 100 = 400pC

Answer 2

Capacitors C1 = 2pF, C2 = 3pF, C3 = 4pF are connected in parallel

Equivalent capacitance of the combination, Ceq is related to C1, C2, C3 as follows:

Ceq = C1 + C2 + C3 = 2 + 3 + 4 = 9pF.

Net charge on the combination, Q = C*V = 9pF*100V = 900pC.

Let charge on capacitor of capacitance C1 be Q1, C2 be Q2 and C3 be Q3.

So, Q1 + Q2 + Q3 = 900pC. …………..(1)

Also, Q1/C1 = Q2/C2 = Q3/C3 = V

So, Q2 = C2*Q1/C1 ……..(2)

Q3 = C3*Q1/C1 ………..(3)

Putting the value of Q2 and Q3 in eq. (1), we get Q1 = 200pC

And finally in eq. (2) and (3), we get Q2 = 300pC and Q3 = 400pC.