What is the total capacitance when three capacitors, C1, C2 and C3 are connected in parallel?

Question

Examoogle · Accepted Answer

$C_1+C_2+C_3$

Explanation: When capacitors are connected in parallel, the total capacitance is equal to the algebraic sum of the individual capacitances. This occurs because the potential difference across each capacitor remains the same, while the total charge stored is the sum of the charges on each capacitor.

Working Principle: In a parallel configuration, the voltage V across each capacitor is identical ($V_1 = V_2 = V_3 = V$). The total charge Q stored in the circuit is the sum of individual charges ($Q_{total} = Q_1 + Q_2 + Q_3$). Since $Q = CV$, substituting this into the charge equation gives $C_{eq}V = C_1V + C_2V + C_3V$, which simplifies to $C_{eq} = C_1 + C_2 + C_3$.

Key Formulas: $C_{eq} = C_1 + C_2 + C_3$ — Total capacitance in parallel; $Q_{total} = Q_1 + Q_2 + Q_3$ — Charge conservation in parallel circuits

Key Points: Capacitors in parallel effectively increase the surface area of the plates.; The total capacitance in parallel is always greater than the largest individual capacitor.; Parallel connection is the dual of series connection for resistors.

Advantages: Increases total energy storage capacity.; Provides redundancy; if one capacitor fails, others remain functional.

Disadvantages: Requires more physical space due to additional components.; Increased total leakage current compared to a single capacitor.

Applications: Power supply filtering to reduce ripple voltage.; Energy storage banks in pulsed power systems.

Additional Info: For series connection, the formula is $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}$.. Option D represents the series connection formula, which is incorrect for this parallel configuration.

Answer: B is correct — For capacitors connected in parallel, the total capacitance is the sum of the individual capacitances.

Exam Tip: Remember: Capacitors in parallel follow the same math as Resistors in series, and vice-versa.

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