Capacitors in Parallel

In parallel, same voltage across each capacitor, charges add. Equivalent capacitance is the sum of all individual capacitances.

Voltage constraint

In parallel, all capacitors share the same two nodes. The potential difference across each is the same: $V_1 = V_2 = \cdots = V_n = V$.

Charge constraint

Total charge drawn from the source:

$$Q = Q_1 + Q_2 + \cdots + Q_n = C_1 V + C_2 V + \cdots + C_n V = V\sum_{i=1}^n C_i$$

Equivalent capacitance

$$C_{eq} = \frac{Q}{V} = \sum_{i=1}^n C_i$$ $$\boxed{C_{eq} = C_1 + C_2 + \cdots + C_n}$$

Key property

$C_{eq} > C_{max}$ — parallel combination is always more capacitive than the largest individual capacitor. Physically: parallel connection increases the effective plate area.

Analogy

Capacitors in series ↔ resistors in parallel (same combination rule for $1/C_{eq}$ and $1/R_{eq}$). Capacitors in parallel ↔ resistors in series (same rule: direct sum).