Electric potential represents electrical “height,” and a capacitor is a device that stores charge. These are fundamental concepts supporting electric circuits.
Basic Knowledge
Electric potential (electric potential, V): Electric potential energy per unit positive charge [J/C = V (volt)]
・Defined using infinity as the reference (V = 0)
・Potential at a distance r from a point charge Q: V = kQ/r
・Potential difference (voltage) = the difference in potential between two points
Relationship between electric field and potential (for a uniform electric field):E = V / d (d: distance, V: potential difference)
Capacitor: A device consisting of two conducting plates facing each other. It stores charge.
・Capacitance (capacitance, C): From Q = CV, C = Q/V [F (farad)]
・Parallel-plate capacitor: C = ε₀ S / d (S: plate area, d: distance between plates)
・Energy stored in a capacitor: U = QV/2 = CV²/2 = Q²/(2C)
Electric potential (V)（electric potential energy per unit positive charge. Unit: V (volt)）
Equipotential surface（a surface connecting points with equal potential. Perpendicular to the electric field）
Capacitor（a device that stores charge. Consists of two conducting plates）
Capacitance (C)（C = Q/V. Unit: F (farad)）
Dielectric（an insulator that increases capacitance when inserted between a capacitor's plates）
Electrostatic energy（energy stored in a capacitor U = CV²/2）
Further Exploration (Background and Significance)
Equipotential surfaces are always perpendicular to the electric field (electric field lines). The electric field points from higher potential to lower potential, just as water flows from a higher place to a lower place. The surface of a conductor is an equipotential surface.
When a dielectric is inserted between the plates of a capacitor, it becomes polarized and weakens the electric field, allowing more charge to be stored at the same voltage. In other words, capacitance C increases. Smartphone touch panels use the principle of capacitors.
Series and parallel connections of capacitors:
・Series connection: 1/C = 1/C₁ + 1/C₂ (the equivalent capacitance becomes smaller than each capacitance)
・Parallel connection: C = C₁ + C₂ (the equivalent capacitance is the sum of the capacitances)
This is the opposite relationship from resistor connections, so care is needed.
- Potential V = kQ/r (from a point charge)
- Electric field and potential: E = V/d
- Capacitor: Q = CV
- Electrostatic energy: U = CV²/2
- Equipotential surface ⊥ electric field lines
- Capacitors in series: 1/C = 1/C₁ + 1/C₂
- Capacitors in parallel: C = C₁ + C₂
Notes (Common Confusions)
① Electric field E is a vector (it has direction), while potential V is a scalar (it has no direction). ② Capacitor connections are the opposite of resistor connections (the equivalent capacitance becomes smaller in series). ③ Do not forget the “1/2” in electrostatic energy U = QV/2. ④ Potential difference = voltage. Distinguish between “potential” and “potential difference (voltage).”
Practice
- A voltage of 12 V is applied to a capacitor with capacitance 4.0 × 10⁻⁶ F. Find the charge stored.
- Find the electrostatic energy stored in the capacitor above.
- State the relationship between equipotential surfaces and electric field lines.