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.
Understanding Engineering: Capacitors and Inductors
A real capacitor has two conducting plates separated by an insulating material called a dielectric. The dielectric may be ceramic, plastic film, paper, or a chemical layer in an electrolytic capacitor. Its material affects how much charge the part can hold, how stable it is with temperature, and how much energy it loses as heat.
Capacitors have voltage ratings because too much electric field can damage the dielectric. Electrolytic capacitors often have polarity, so connecting one backwards can cause heating, leakage, or failure. Small ceramic capacitors are common near computer chips because they supply brief bursts of current when a chip switches.
An inductor is usually a length of wire wound into turns. More turns and a magnetic core can increase its inductance. Cores made from ferrite or iron guide magnetic fields, but they have limits.
At high current, a core can saturate. Once saturated, it cannot store much additional magnetic energy, and current can rise rapidly. The wire itself has resistance, which causes heat.
Coils can create unwanted magnetic fields that affect nearby circuits, so engineers consider placement and shielding. Inductors appear in phone chargers, LED drivers, motor controllers, and switching power supplies.
The most important behavior appears when a circuit changes state. When a switch closes, a capacitor does not instantly reach its final voltage. It charges over time through the available resistance.
A larger capacitance or resistance makes this process slower. An inductor behaves differently during the same event. Its current builds gradually, which can protect a circuit from a sudden current rise.
When current through an inductor is interrupted, the stored field tries to keep current flowing. This can produce a large voltage spike. A diode placed across a relay coil gives that current a safe path and prevents damage to a transistor.
Capacitors and inductors respond differently at different frequencies. A capacitor can provide an easier path for rapidly changing signals than for steady voltage. This is why it can block the direct current part of an audio signal while passing the changing audio part to the next stage.
An inductor tends to oppose rapidly changing current more strongly. Combining these parts with resistors creates filters that select low, high, or narrow ranges of frequencies. In a resonant circuit, energy moves back and forth between the capacitor and inductor.
Radios use this effect to select stations. When studying circuits, track the direction of current, the polarity of voltage, the switch position, and whether the circuit has just changed or has been left connected for a long time.
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.