Mastering Ohm’s Law
Visualize the fundamental relationship between Voltage, Current, and Resistance. Explore how these principles apply to real-world components like resistors, capacitors, and inductors.
1. The Water Pipe Analogy
To understand electrical circuits, imagine water flowing through a system of pipes:
- Voltage (V): The water pressure pushing the water through the pipe.
- Current (I): The actual flow rate of the water.
- Resistance (R): The thickness of the pipe or any obstructions inside it.
2. Definition of Ohm’s Law
Ohm’s Law states that the electrical current flowing through a linear conductor is strictly proportional to the voltage across it, assuming temperature remains constant.
Where: V = Voltage (Volts), I = Current (Amperes), R = Resistance (Ohms)
3. Ohm’s Law Interactive Simulation
Adjust the sliders below. The Wire Animation shows how resistance restricts flow. The V-I Graph demonstrates that resistance acts as a constant slope determining current.
Wire Cross-Section
V-I Characteristic Curve
4. Where to Apply (and Not Apply) Ohm’s Law
✔ Where to Apply
- Purely resistive circuits: Standard resistors and heating elements.
- DC Circuits: Calculating steady-state voltage drops.
✘ Where NOT to Apply
- Non-linear devices: Diodes, transistors, and LEDs.
- Dynamic Components: Capacitors and Inductors during charge states.
5. Capacitor Working Principle
A capacitor stores energy in an electric field between two plates. When voltage is applied, charge ($Q$) accumulates on the plates, causing voltage to rise over time. The speed of this charge/discharge process is determined by the Time Constant (τ)—the time required to charge to 63.2%.
Capacitor Voltage over Time
6. Inductor Working Principle
An inductor stores energy in a magnetic field generated by current flowing through a coil. According to Lenz’s Law, it fundamentally opposes any *change* in current. When voltage is applied, the magnetic field slowly builds, restricting current flow initially. The Time Constant (τ) defines how quickly this field stabilizes.
Inductor Current over Time
7. Why Ohm’s Law Fails for Capacitors & Inductors
Standard Ohm’s Law requires a constant ratio between Voltage and Current. However, in these dynamic components, V and I change at completely different rates over time. Plotting the instantaneous ratio (V/I) during a DC step yields a constantly changing curve, proving standard Ohm’s law ($V=IR$) cannot be applied. We must use Impedance (Z) instead.
8. Summary
Ohm’s Law (V = I × R) defines the static relationship between voltage, current, and resistance in linear components. With dynamic components like Capacitors and Inductors, Resistance (R) is replaced by Impedance (Z), modifying the law to V = I × Z to account for time dependency.