Three capacitors of 3, 2 and 6μF connected in series with a battery of 10V. Then charge on 3μF capacitor will be:

CONCEPT:

• The capacitance of a capacitor (C): The capacity of a capacitor to store the electric charge is called capacitance.
  • The capacitance of a conductor is the ratio of charge (Q) to it by a rise in its potential (V).

​C = Q/V

• The unit of capacitance is the farad, (symbol F ).
• Series combination: When two or more capacitors are connected end to end and have the same electric charge on each is called the series combination of the capacitor.

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• Equivalent capacitance (Ceq) in series combination:

\(\frac{1}{{{C_{eq}}}} = \frac{1}{{{C_1}}} + \frac{1}{{{C_2}}} + \frac{1}{{{C_3}}}\)

CALCULATION:

​Given that:

C₁ = 3 μF, C2 = 2 μF, and C3 = 6 μF

Potential of the battery (V) = 10 V

They are in series combination:

So \(\frac{1}{{{C_{eq}}}} = \frac{1}{{{C_1}}} + \frac{1}{{{C_2}}} + \frac{1}{{{C_3}}}\)

\(\frac{1}{{{C_{eq}}}} = \frac{1}{{{3}}} + \frac{1}{{{2}}} + \frac{1}{{{6}}} =\frac{2 + 3 +1}{6}=\frac{6}{6}= 1\)

C_eq = 1 μF

Charge (Q) = C V = 1 × 10 = 10 μC

Since they are in series combination, so the charge on each capacitor will be the same.

So charge on 3 μF = 10 μC

Hence option 1 is correct.

EXTRA POINTS:

• Parallel combination: When two or more capacitors are connected in such a way that their ends are connected at the same two points and have an equal potential difference for all capacitor is called a parallel combination of the capacitor.

• Equivalent capacitance (Ceq) for parallel combination:

Ceq = C1 + C2 + C3

Where C1 is the capacitance of the first capacitor, C2 is the capacitance of the second capacitor and C3 is the capacitance of the third capacitor