use the capacitance formulae for capacitors in series and in parallel

Capacitors and Capacitance

What is a Capacitor?

A capacitor is like a tiny water tank that stores electric charge instead of water. The two plates are the tank walls, and the electric field between them is the water pressure that pushes charge.

Capacitance Formula

The ability of a capacitor to store charge is measured by its capacitance C:

$C = \dfrac{Q}{V}$

where Q is the charge in coulombs and V is the voltage across the plates.

For a parallel‑plate capacitor:

$C = \epsilon_0 \dfrac{A}{d}$

• A = area of the plates (m²)
• d = separation between plates (m)
• ε₀ = vacuum permittivity ≈ 8.85×10⁻¹² F/m

Capacitors in Parallel

When capacitors are connected side‑by‑side, the voltage across each is the same, but the total charge adds up.

$C_{\text{eq,\,parallel}} = C_1 + C_2 + C_3 + \dots$

Think of it as multiple water tanks connected to the same water source; each tank fills with the same pressure, but the total water stored is the sum.

Capacitors in Series

When capacitors are connected end‑to‑end, the charge on each is the same, but the voltage divides.

$\displaystyle \frac{1}{C_{\text{eq,\,series}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \dots$

Analogy: Imagine a chain of water tanks where the same amount of water flows through each. The total height (voltage) is split across the tanks.

Quick Reference Table

Example Problem (Parallel)

1. Two capacitors: $C_1 = 4\,\mu\text{F}$, $C_2 = 6\,\mu\text{F}$.
2. Connected in parallel.
3. Find $C_{\text{eq}}$.

Solution: $C_{\text{eq}} = 4 + 6 = 10\,\mu\text{F}$.

Example Problem (Series)

1. Two capacitors: $C_1 = 3\,\mu\text{F}$, $C_2 = 12\,\mu\text{F}$.
2. Connected in series.
3. Find $C_{\text{eq}}$.

Solution:

$\displaystyle \frac{1}{C_{\text{eq}}} = \frac{1}{3} + \frac{1}{12} = \frac{4}{12} + \frac{1}{12} = \frac{5}{12}$
$C_{\text{eq}} = \frac{12}{5} = 2.4\,\mu\text{F}$

Key Takeaway

Capacitance is a measure of how much charge a capacitor can store per volt. By arranging capacitors in series or parallel, you can tailor the total capacitance to fit the needs of a circuit—just like arranging water tanks to store more or less water.