The effective capacitance of a capacitor is reduced when capacitors are connected in: A. series-parallel combination B. parallel C. Series none of the these D
The Correct Answer and Explanation is:
Correct Answer: C. Series
Explanation:
When capacitors are connected in different configurations, their effective capacitance—which is the total capacitance of the entire system—changes depending on how they are arranged.
1. Capacitors in Series:
When capacitors are connected in series, the total or effective capacitance decreases. The formula used to calculate the total capacitance CeqC_{\text{eq}}Ceq of capacitors in series is:1Ceq=1C1+1C2+1C3+⋯\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \cdotsCeq1=C11+C21+C31+⋯
This is because the charge on each capacitor is the same, but the voltage is divided among the capacitors. Since the reciprocal of the total capacitance is equal to the sum of the reciprocals of individual capacitances, the result is always smaller than the smallest individual capacitor in the series. This configuration is similar to adding resistors in parallel.
Example:
If you connect three capacitors of 6 µF, 3 µF, and 2 µF in series, the effective capacitance is:1Ceq=16+13+12=1+2+36=66=1⇒Ceq=1μF\frac{1}{C_{\text{eq}}} = \frac{1}{6} + \frac{1}{3} + \frac{1}{2} = \frac{1+2+3}{6} = \frac{6}{6} = 1 \Rightarrow C_{\text{eq}} = 1 \mu FCeq1=61+31+21=61+2+3=66=1⇒Ceq=1μF
2. Capacitors in Parallel:
In contrast, when capacitors are connected in parallel, their total capacitance is the sum of individual capacitances:Ceq=C1+C2+C3+⋯C_{\text{eq}} = C_1 + C_2 + C_3 + \cdotsCeq=C1+C2+C3+⋯
So, the effective capacitance increases in parallel combination.
3. Series-Parallel Combination:
In a series-parallel arrangement, some capacitors are in series and others in parallel. The resulting capacitance depends on the specific layout, but it is generally between the values you would get from pure series or pure parallel connections.
Conclusion:
The effective capacitance decreases only in the series arrangement of capacitors. Therefore, the correct answer is:
✅ C. Series
