Three capacitors: 3.0 μF, 5.0 μF and 7.0 μF are connected in series and in parallel. The equivalent capacitance in series and parallel are ……….
Question
Three capacitors: 3.0 μF, 5.0 μF and 7.0 μF are connected in series and in parallel. The equivalent capacitance in series and parallel are ……….
Solution
For capacitors, the total capacitance (Ct) in a series circuit is calculated differently than in a parallel circuit.
- In a series circuit, the total capacitance is given by the reciprocal of the sum of the reciprocals of the individual capacitances.
Formula: 1/Ct = 1/C1 + 1/C2 + 1/C3
Substituting the given values:
1/Ct = 1/3.0 + 1/5.0 + 1/7.0 1/Ct = 0.333 + 0.2 + 0.143 1/Ct = 0.676
Therefore, Ct = 1 / 0.676 = 1.48 μF
- In a parallel circuit, the total capacitance is simply the sum of the individual capacitances.
Formula: Ct = C1 + C2 + C3
Substituting the given values:
Ct = 3.0 + 5.0 + 7.0 Ct = 15.0 μF
So, the equivalent capacitance when the capacitors are connected in series is 1.48 μF and when connected in parallel is 15.0 μF.
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