Question:
When two capacitors of capacities $C_{1}$ and $C_{2}$ are connected in parallel, the equivalent capacitance is
When two capacitors of capacities $C_{1}$ and $C_{2}$ are connected in parallel, the equivalent capacitance is
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Capacitor rules are the exact \textbf{opposite} of resistor rules. Capacitors add in parallel ($C_1+C_2$) and follow the reciprocal rule in series. Resistors add in series ($R_1+R_2$) and follow the reciprocal rule in parallel.
Updated On: Apr 24, 2026
- $C_{1}+C_{2}$
- $\frac{C_{1}C_{2}}{C_{1}+C_{2}}$
- $\frac{C_{1}+C_{2}}{C_{1}C_{2}}$
- $\sqrt{C_{1}C_{2}}$
- $C_{1}-C_{2}$
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The Correct Option is A
Solution and Explanation
Concept:
Physics - Combination of Capacitors.
Step 1: Analyze the parallel connection.
In a parallel connection, the potential difference ($V$) across each capacitor is the same. [Image of capacitors in parallel connection]
Step 2: Consider the charge storage.
The total charge ($Q$) supplied by the source is shared between the capacitors: $$ Q = Q_1 + Q_2 $$
Step 3: Substitute the capacitance formula ($Q=CV$).
$$ C_{eq}V = C_1V + C_2V $$
Step 4: Simplify the equation.
Divide the entire equation by $V$: $$ C_{eq} = C_1 + C_2 $$ The equivalent capacitance is the simple sum of individual capacitances.
Physics - Combination of Capacitors.
Step 1: Analyze the parallel connection.
In a parallel connection, the potential difference ($V$) across each capacitor is the same. [Image of capacitors in parallel connection]
Step 2: Consider the charge storage.
The total charge ($Q$) supplied by the source is shared between the capacitors: $$ Q = Q_1 + Q_2 $$
Step 3: Substitute the capacitance formula ($Q=CV$).
$$ C_{eq}V = C_1V + C_2V $$
Step 4: Simplify the equation.
Divide the entire equation by $V$: $$ C_{eq} = C_1 + C_2 $$ The equivalent capacitance is the simple sum of individual capacitances.
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