Question

3 condensers of capacitance 3F,6F,9F are connected (i) in series and (ii)in parallel .Compare the equivalent capacitance in two cases​

Answer 1

Answer :

• The equivalent capacitance in the series combination of capacitance 3 F, 6 F and 9 F is 1.64 F.

• The equivalent capacitance in the parallel combination of capacitance 3 F, 6 F and 9 F is 18 F.

Explanation :

Given :

• Capacitance of the condenser, C1 = 3 F

• Capacitance of the condenser, C2 = 6 F

• Capacitance of the condenser, C3 = 9 F

To find :

• The equivalent capacitance in the series combination.

• The equivalent capacitance in the parallel combination.

Knowledge required :

• Formula for equivalent capacitance in a parallel combination :

⠀⠀⠀⠀⠀⠀⠀⠀⠀Cr = C1 + C2 + C3 + ... + Cn

Where :

• Cr = Equivalent capacitance in the parallel combination.

• C = Capacitance in the condenser.

• Formula for equivalent capacitance in a Series combination :

⠀⠀⠀⠀⠀1/Cr = 1/C1 + 1/C2 + 1/C3 + ... + 1/Cn

Where :

• Cr = Equivalent capacitance in the parallel combination.

• C = Capacitance in the condenser.

Solution :

Equivalent capacitance in the series combination :

By using the formula for Equivalent capacitance in a series combination and substituting the values in it , we get :

==> 1/Cr = 1/C1 + 1/C2 + 1/C3

==> 1/Cr = 1/3 + 1/6 + 1/9

==> 1/Cr = (6 + 3 + 2)/18

==> 1/Cr = 11/18

==> Cr = 18/11

==> Cr = 1.64 (approx.)

∴ Cr = 1.64 F

Equivalent capacitance in the parallel combination :

By using the formula for Equivalent capacitance in a series combination and substituting the values in it , we get :

==> Cr = C1 + C2 + C3

==> Cr = 3 + 6 + 9

==> Cr = 18

∴ Cr = 18 F

Therefore,

• The equivalent capacitance in the series combination is 18/11 F.

• The equivalent capacitance in the parallel combination is 18 F.