Capacitors and inductors are two basic circuit components that store energy instead of simply dissipating it. A capacitor stores energy in the electric field between separated charges, while an inductor stores energy in the magnetic field created by current through a coil. These parts matter because they control timing, filtering, energy transfer, and signal shape in almost every electronic system.
They are essential in power supplies, radios, sensors, motors, and communication circuits.
Their behavior is described by relationships between voltage and current that involve rates of change. For a capacitor, current depends on how quickly the voltage changes, so it strongly affects sudden voltage transitions. For an inductor, voltage depends on how quickly the current changes, so it resists sudden current transitions.
Together, capacitors and inductors can form oscillators, filters, and resonant circuits that exchange energy between electric and magnetic fields.
Key Facts
- Capacitor current-voltage relationship: i = C dv/dt.
- Inductor voltage-current relationship: v = L di/dt.
- Energy stored in a capacitor: U = 1/2 C V^2.
- Energy stored in an inductor: U = 1/2 L I^2.
- RC time constant: tau = RC, and RL time constant: tau = L/R.
- In DC steady state, an ideal capacitor acts like an open circuit and an ideal inductor acts like a short circuit.
Vocabulary
- Capacitance
- Capacitance is the ability of a component to store electric charge per volt, measured in farads.
- Inductance
- Inductance is the ability of a component to oppose changes in current by producing a voltage, measured in henrys.
- Electric field
- An electric field is a region where electric charges experience a force, such as the field between capacitor plates.
- Magnetic field
- A magnetic field is a region produced by moving charge or current, such as the field around an inductor coil.
- Time constant
- A time constant describes how quickly voltage or current changes in a first-order circuit after a switch or input change.
Common Mistakes to Avoid
- Treating a capacitor as a resistor is wrong because a capacitor's current depends on dv/dt, not directly on voltage.
- Assuming capacitor voltage changes instantly is wrong because changing voltage across a capacitor requires current over time.
- Assuming inductor current changes instantly is wrong because an inductor produces voltage that opposes rapid current changes.
- Forgetting steady-state behavior is wrong because after a long time in a DC circuit, an ideal capacitor blocks current while an ideal inductor conducts like a wire.
Practice Questions
- 1 A 10 microfarad capacitor is charged to 12 V. How much energy is stored in it?
- 2 A 50 millihenry inductor carries a current of 2.0 A. How much energy is stored in its magnetic field?
- 3 A switch connects a resistor and capacitor in series to a DC battery. Explain why the current is largest just after the switch closes and becomes nearly zero after a long time.