Question

1-Derive the capacitance in 3 capacitors, C1, C2, and C3 in series.

2-Derive the capacitence in 3 capacitors C1, C2, C3 in parallel.

Answer 1

1) in series :-

Let the Charge flowing through these capacitors be Q.and in series Circuit the charge remains same.
Let V1 be the Voltage Across C1
V2 be the voltage across C2
V3 be the voltage across C3

Since, V = Q / C .......(1)

as voltage of the source is divided among all the three capacitors.so,

V = V1 + V2 + V3 .......(2)

using equation (1) in equation (2),

Q/C = Q/C1 + Q/C2 + Q/C3

Q/C = Q [ 1/C1 + 1/C2 + 1/C3]

1/C = 1/C1 + 1/C2 + 1/C3

2) in parallel :-

Let the voltage source across these capacitors is V.as voltage remains equal in the parallel circuit.

let the charge flowing through capacitor C1 be Q1.

the charge flowing through capacitor C2 be Q2,

the charge flowing through capacitor C3 be Q3.

now the total charge Q is divided among three capacitors as Q1,Q2 and Q3.

Q = Q1 + Q2 + Q3 .....(3)

as Q = C*V .....(4)

using equation (4) in equation (3),

C*V = C1*V + C2*V + C3*V

C*V = V [ C1 + C2 + C3]

C = C1 + C2 + C3

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