Upon successful completion of this module, the student will be able to:
Describe the construction and function of a capacitor and an inductor.
Explain the process of charging and discharging a capacitor in a DC circuit.
Explain how an inductor stores energy and opposes changes in current in a DC circuit.
Calculate the RC and RL time constants and predict circuit behavior after one and five time constants.
Apply knowledge of capacitors and inductors to troubleshoot common timing and energy storage circuits.
So far, we've dealt with circuits that react instantly. Flip a switch, and the light comes on. But what about the circuits that have a sense of time? The dome light in your car that gently fades out, the delay before a machine starts, or the massive burst of energy needed for a spark plug—these effects are all created by two fascinating components: capacitors and inductors.
These aren't like resistors, which simply burn off energy as heat. Capacitors and inductors store energy and release it in unique ways, allowing us to shape, delay, and control electricity like never before. Mastering them is key to understanding everything from timing circuits to power supplies.
Capacitors: The Tiny, Fast-Recharging Battery
A capacitor stores energy in an electric field. Think of it as a small water tower or a tiny battery that can charge and discharge almost instantly.
How it Works: It's made of two metal plates separated by an insulator (a dielectric). When you apply a DC voltage, electrons pile up on one plate, forcing electrons off the other. This creates a potential difference—a stored charge.
Charging: In a simple RC (Resistor-Capacitor) circuit, the capacitor doesn't charge instantly. The resistor limits the flow of current, so the capacitor's voltage ramps up over time until it matches the source voltage.
Discharging: Once charged, if you provide a path, the capacitor will release all its stored energy in a burst, with the current flowing in the opposite direction.
The Familiar Example: The Dome Light Fade-Out. This is a perfect real-world RC circuit. When you shut the car door, instead of cutting power instantly, the circuit lets a charged capacitor discharge through the dome light. As the capacitor's voltage slowly fades to zero, the light dims smoothly along with it.
Inductors: The Electrical Flywheel
An inductor stores energy in a magnetic field. If a capacitor is like a water tower (storing potential), an inductor is like a heavy water wheel or flywheel—it's all about motion and momentum.
How it Works: It's just a coil of wire. When current flows through it, a magnetic field builds up around the coil.
The Key Property: Opposing Change. An inductor hates changes in current.
When you first apply power, the inductor's building magnetic field creates a counter-voltage that opposes the current, so the current ramps up slowly.
If you then try to stop the current, the inductor's collapsing magnetic field creates a forward-voltage that tries to keep the current flowing.
The Familiar Example: The Ignition Coil. A car's ignition coil is a massive inductor. It "charges" by building up a powerful magnetic field. When the circuit is suddenly broken, that collapsing field has nowhere to go and creates a huge voltage spike (thousands of volts). This spike is what's powerful enough to jump the gap on a spark plug, igniting the fuel.
Both RC and RL circuits have a "time constant," represented by the Greek letter Tau (τ). It's the fundamental unit of time that governs how fast they charge or discharge.
For Capacitors (RC Circuit): τ = R * C (Resistance in Ohms × Capacitance in Farads)
For Inductors (RL Circuit): τ = L / R (Inductance in Henrys / Resistance in Ohms)
The Universal Rule of Five:
For both types of circuits, the "magic number" is five. A circuit is considered fully charged or fully discharged after five time constants (5τ). After just one time constant (1τ), it will have completed about 63.2% of its change.
Example Calculation:
You have a simple timer circuit with a 4.7kΩ (4700Ω) resistor and a 100µF (0.0001F) capacitor.
τ = 4700 * 0.0001 = 0.47 seconds
Full charge time = 5 * 0.47s = 2.35 seconds
This means it will take about 2.35 seconds for the capacitor to fully charge and trigger whatever device is connected to it.
The Problem: "Inductive Kick"
You've seen a small spark when you unplug a running vacuum cleaner, right? That's inductive kick! When you de-energize an inductive load like a motor or a solenoid valve, its collapsing magnetic field generates a massive voltage spike. In sensitive electronics, this spike can be deadly, destroying transistors and microchips.
The Analysis: A technician knows this spike is a predictable property of an inductor. The energy stored in the magnetic field has to go somewhere.
The Solution: We can evaluate this problem and solve it by adding a simple component: a flyback diode. This diode is placed in parallel with the inductor. It does nothing during normal operation, but when the power is cut, it provides a safe, closed loop for the inductor's stored energy to circulate and dissipate harmlessly instead of creating a damaging voltage spike.
The Scenario: A customer has a vintage amplifier where the "soft start" feature is broken. When they turn it on, it makes a loud "pop" instead of fading in the sound. You know this is a timing circuit, likely involving a capacitor.
Your Diagnostic Plan:
Hypothesis: The "pop" suggests the timing function is gone. This is likely due to a faulty capacitor in the RC timing circuit. The capacitor has probably failed short, meaning it acts like a simple wire and can't store a charge.
Create a Test Plan (In-Circuit):
Safety: Unplug the amplifier completely.
Identify: Locate the likely timing capacitor on the circuit board (often near a relay).
Test: Set your multimeter to measure resistance (Ohms). Place your leads across the capacitor.
Expected Result (Good Capacitor): The resistance should start low and then climb steadily towards infinite ("OL") as the multimeter's own small voltage charges the capacitor.
The Fault Finding: In this case, you measure a resistance of near 0Ω that doesn't change. This confirms your hypothesis: the capacitor is internally shorted. It cannot charge, so the timing circuit activates instantly, causing the "pop." You have successfully diagnosed the root cause.
(Remembering)
A capacitor stores energy in an __ field, while an inductor stores energy in a __ field.
What is the "rule of thumb" for how many time constants it takes for an RC or RL circuit to be considered fully charged or discharged?
(Understanding)
3. Explain why a large inductor in series with a light bulb will cause the bulb to be slightly delayed in reaching its full brightness.
4. A technician builds a dome light fade-out circuit. If they use a capacitor with a larger capacitance value, will the fade-out effect be longer or shorter? Explain why.
(Applying)
5. What is the time constant (τ) of a series circuit with a 2.2kΩ resistor and a 470µF capacitor?
6. An RL circuit has a time constant of 25ms. Approximately how long will it take for the current to reach its maximum steady-state value?
(Analyzing)
7. A technician sees a prominent spark jump across a switch's contacts every time they de-energize a large solenoid. Analyze this situation and identify the electrical principle and the component type responsible for the spark.
8. A simple industrial timer uses an RC circuit to delay the activation of a 12V relay. The relay requires at least 7.5V to turn on. After one time constant, a capacitor charges to about 63.2% of the source voltage. Analyze whether the relay will activate before or after one time constant has passed.
(Evaluating)
9. A circuit design requires a short time delay. You have two capacitors (100µF and 470µF) and two resistors (1kΩ and 10kΩ). Which combination of one capacitor and one resistor would you choose to create the shortest possible time constant? Justify your choice.
(Creating)
10. The horn on a golf cart is intermittent. You suspect the capacitor in the horn's power circuit (which helps provide the initial burst of energy) is failing. Create a simple, safe test plan to determine if the capacitor is "leaky" (unable to hold its charge for a reasonable time).
Various circuits using basic electrical kits, mobile modular, control circuit panels