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Eight capacitors of the same value are connected in series. Their equivalent capacitance is 200µF, the capacitance of each capacitor is _________.
25 µF
16 µF
160 µF
16 × 10⁻⁴ F
16 × 10⁻⁴ F
When n identical capacitors are connected in series, the equivalent capacitance Ceq is given by the capacitance of one unit C divided by the number of units n. Given Ceq=200 µF and n=8, the individual capacitance is C=n×Ceq=8×200 µF=1600 µF.
When n identical capacitors are connected in series, the equivalent capacitance Ceq is given by the capacitance of one unit C divided by the number of units n. Given Ceq=200 µF and n=8, the individual capacitance is C=n×Ceq=8×200 µF=1600 µF.
Ceq=nC — Equivalent capacitance for n identical capacitors in series.
C=n×Ceq — Formula to calculate individual capacitance from series equivalent.
In a series circuit, the total voltage divides across capacitors, reducing the overall charge storage capacity per unit potential. The reciprocal of the equivalent capacitance equals the sum of the reciprocals of individual capacitances. For identical capacitors, this simplifies to the relation Ceq=C/n.
Series connection of capacitors increases the effective voltage rating but decreases total capacitance.
The total capacitance in series is always less than the smallest individual capacitor value.
The value 1600 µF is equivalent to 16×10−4 F since 1 µF=10−6 F.
Increased breakdown voltage rating of the bank.
Reduction in total leakage current due to voltage division.
Reduced overall storage capacity.
Requires high voltage insulation if capacitors are mismatched.
High-voltage capacitor banks.
Voltage grading in power electronic circuits.
Calculation: 1600×10−6 F=1.6×10−3 F=16×10−4 F.
Option A is 25 µF, which corresponds to the case if they were in parallel (Ceq=n×C).
Option C is 160 µF, which is a calculation error ignoring the series scaling factor.
D is correct — The individual capacitance is 1600 µF, which converts to 16×10−4 F.
Always check unit prefixes carefully during conversion; 1 µF=10−6 F. Remember that series capacitors behave like parallel resistors.
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