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