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Three capacitors of capacitances $2 \mathrm{pF}, 3 \mathrm{pF}$ and $4 \mathrm{pF}$ are connected in parallel.
(a) What is the total capacitance of the combination?
(b) Determine the charge on each capacitance if the combination is connected to a $100 \mathrm{~V}$ supply.
(a) What is the total capacitance of the combination?
(b) Determine the charge on each capacitance if the combination is connected to a $100 \mathrm{~V}$ supply.
Solution:
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Verified Answer
Given, $\mathrm{C}_1=2 \mathrm{pF}, \mathrm{C}_2=3 \mathrm{pF}, \mathrm{C}_3=4 \mathrm{pF}$,
(a) $\mathrm{C}_{\mathrm{p}}=$ ?, (b) $\mathrm{V}=100 \mathrm{~V}, \mathrm{q}_1=$ ?, $\mathrm{q}_2=$ ?,
$\mathrm{q}_3=$ ?
(a) By formula, in parallel combination,
$\mathrm{C}_{\mathrm{p}}=\mathrm{C}_1+\mathrm{C}_2+\mathrm{C}_3=2+3+4=9 \mathrm{pF}$
(b) In parallel combination, potential difference is same across each capacitor.
By relation, $\mathrm{q}=\mathrm{CV}$. Substituting the values,
we get, $\mathrm{q}_1=2 \times 100=200 \mathrm{pC}$
$$
\begin{gathered}
=200 \times 10^{-12} \mathrm{C} \\
\mathrm{q}_2=3 \times 100=300 \mathrm{pC}=300 \times 10^{-12} \mathrm{C} \\
\mathrm{q}_3=4 \times 100=400 \mathrm{pC}=400 \times 10^{-12} \mathrm{C} .
\end{gathered}
$$
(a) $\mathrm{C}_{\mathrm{p}}=$ ?, (b) $\mathrm{V}=100 \mathrm{~V}, \mathrm{q}_1=$ ?, $\mathrm{q}_2=$ ?,
$\mathrm{q}_3=$ ?
(a) By formula, in parallel combination,
$\mathrm{C}_{\mathrm{p}}=\mathrm{C}_1+\mathrm{C}_2+\mathrm{C}_3=2+3+4=9 \mathrm{pF}$
(b) In parallel combination, potential difference is same across each capacitor.
By relation, $\mathrm{q}=\mathrm{CV}$. Substituting the values,
we get, $\mathrm{q}_1=2 \times 100=200 \mathrm{pC}$
$$
\begin{gathered}
=200 \times 10^{-12} \mathrm{C} \\
\mathrm{q}_2=3 \times 100=300 \mathrm{pC}=300 \times 10^{-12} \mathrm{C} \\
\mathrm{q}_3=4 \times 100=400 \mathrm{pC}=400 \times 10^{-12} \mathrm{C} .
\end{gathered}
$$
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