recall and use C = Q / V

Capacitors and Capacitance

Capacitance is the ability of a component to store electric charge. Think of it as a water tank that can hold a certain amount of water (charge) for a given pressure (voltage). The larger the tank, the more water it can hold for the same pressure.

Key Formula

The fundamental relationship is \$C = \dfrac{Q}{V}\$ where:

  • \$C\$ = capacitance (Farads, F)

  • \$Q\$ = charge stored (Coulombs, C)

  • \$V\$ = voltage across the capacitor (Volts, V)

Parallel‑Plate Capacitor Example

For a parallel‑plate capacitor:

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

  • \$\varepsilon\$ = permittivity of the dielectric (\$\varepsilon0 \varepsilonr\$)

  • \$A\$ = area of the plates (m²)

  • \$d\$ = separation between plates (m)

⚡️ Analogy: Imagine two flat plates as the sides of a sandwich. The larger the sandwich (area), the more space for charge. The closer the plates (smaller d), the stronger the electric field, so more charge can be stored for the same voltage.

Example Calculation

  1. Given: \$A = 0.02\ \text{m}^2\$, \$d = 0.001\ \text{m}\$, \$\varepsilon_r = 2.5\$ (relative permittivity). Find \$C\$.

  2. Compute \$\varepsilon = \varepsilon0 \varepsilonr = (8.85\times10^{-12}\ \text{F/m}) \times 2.5 = 2.21\times10^{-11}\ \text{F/m}\$.

  3. Plug into \$C = \dfrac{\varepsilon A}{d}\$: \$C = \dfrac{2.21\times10^{-11}\ \text{F/m} \times 0.02\ \text{m}^2}{0.001\ \text{m}} = 4.42\times10^{-10}\ \text{F} = 442\ \text{pF}\$.

Series & Parallel Capacitors

ConfigurationEffective Capacitance
Parallel\$C{\text{eq}} = C1 + C_2 + \dots\$
Series\$\displaystyle \frac{1}{C{\text{eq}}} = \frac{1}{C1} + \frac{1}{C_2} + \dots\$

Exam Tips

🔍 Tip 1: Always check the units – Farads are SI, but you may need to convert pF, nF, µF, mF.

🔍 Tip 2: When a problem gives charge and voltage, use \$C = Q/V\$ directly. If it gives area, separation, and dielectric, use \$C = \varepsilon A/d\$.

🔍 Tip 3: For series/parallel, write down the formula first, then plug in the numbers.

🔍 Tip 4: Remember the energy stored: \$U = \dfrac{1}{2} C V^2\$. This can help check your answer if a problem mentions energy.

Quick Quiz

  1. What is the capacitance of a 10 µF capacitor charged to 5 V? (Answer: 2 µC)

  2. Two capacitors, 4 µF and 6 µF, are connected in parallel. What is the total capacitance? (Answer: 10 µF)

  3. Two capacitors, 4 µF and 6 µF, are connected in series. What is the total capacitance? (Answer: 2.4 µF)