Question

Three capacitors of capacitances 10 \(\mu\)F, 5 \(\mu\)F and 20 \(\mu\)F are connected in series with a 14 V dc supply. The charge on 5 \(\mu\)F capacitor is

• A. 20 \(\mu\)C
• B. 40 \(\mu\)C
• C. 70 \(\mu\)C
• D. 2.8 \(\mu\)C

Hint:

When capacitors are connected in series, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances.

Answer 1

The Correct Option is B

When capacitors are connected in series, the charge on each capacitor is the same. The equivalent capacitance of the series combination is \[\frac{1}{C} = \frac{1}{10} + \frac{1}{5} + \frac{1}{20} = \frac{2 + 4 + 1}{20} = \frac{7}{20},\]so \(C = \frac{20}{7} \, \mu\)F. The charge on this equivalent capacitor is \[ Q = CV = \frac{20}{7} \times 14 = 40 \, \mu C. \] This is also the charge on the \( 5 \, \mu F \) capacitor.