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Home » Three capacitors of capacitances and are connected in parallel. (1) What is the total capacitance of the combination? (2) Determine the charge on each capacitor if the combination is connected to a supply.
Three capacitors of capacitances 2 \mathrm{pF}, 3 \mathrm{pF} and 4 \mathrm{pF} are connected in parallel.
(1) What is the total capacitance of the combination?
(2) Determine the charge on each capacitor if the combination is connected to a 100 \mathrm{~V} supply.
CBSE | Class 12 | Electrostatic Potential and Capacitance | NCERT | Physics
Three capacitors of capacitances 2 \mathrm{pF}, 3 \mathrm{pF} and 4 \mathrm{pF} are connected in parallel.
(1) What is the total capacitance of the combination?
(2) Determine the charge on each capacitor if the combination is connected to a 100 \mathrm{~V} supply.

Solution:

(1) Given, C_{1}=2 p F, C_{2}=3 p F and C_{3}=4 p F.

Equivalent capacitance for the parallel combination is given by \mathrm{C}_{\mathrm{eq}}.

Therefore, \mathrm{C}{\mathrm{eq}}=\mathrm{C}{1}+\mathrm{C}{2}+\mathrm{C}{3}=2+3+4=9 \mathrm{pF}

Hence, the total capacitance of the combination is 9 \mathrm{pF}.

(2) Supply voltage, V=100 \mathrm{~V}

The three capacitors have the same voltage as one another, V=100 v

We know that, q=V C

where, q= charge : C= capacitance of the capacitor
V= potential difference

For capacitance, c=2 \mathrm{pF}

q=100 \times 2=200 \mathrm{pC}=2 \times 10^{-10} \mathrm{C}

for capacitance, c=3 \mathrm{pF}

q=100 \times 3=300 \mathrm{pC}=3 \times 10^{-10} \mathrm{C}

for capacitance, c=4 \mathrm{pF}

q=100 \times 4=400 \mathrm{pC}=4 \times 10^{-10} \mathrm{C}

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