Ohm's Law

Electricity
definition

Also known as: V=IR, voltage-current relationship

Grade 9-12

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The fundamental relationship stating that the voltage (V) across an ohmic conductor equals the current (I) flowing through it multiplied by its resistance (R). Ohm's law is the single most-used equation in circuit analysis and electrical engineering.

Definition

The fundamental relationship stating that the voltage (V) across an ohmic conductor equals the current (I) flowing through it multiplied by its resistance (R).

💡 Intuition

More push (voltage) means more flow (current). More resistance means less flow for the same push.

🎯 Core Idea

Voltage, current, and resistance are linked — knowing any two lets you calculate the third.

Example

A 12 V battery connected to a 4 \Omega resistor: I = \frac{12}{4} = 3 A.

Formula

V = IR or equivalently I = \frac{V}{R} or R = \frac{V}{I}

Notation

V is the potential difference in volts (V), I is the current in amperes (A), R is the resistance in ohms (\Omega), \vec{J} is the current density in A/m², and \sigma is the electrical conductivity in S/m.

🌟 Why It Matters

Ohm's law is the single most-used equation in circuit analysis and electrical engineering. It is essential for calculating current draw, sizing wires, designing circuits, troubleshooting faults, and ensuring electrical safety in homes and industry.

💭 Hint When Stuck

When solving an Ohm's law problem, first identify the component you are analysing and determine which two of the three quantities (V, I, R) you know. Then rearrange the formula to solve for the unknown: V = IR, I = V/R, or R = V/I. Apply the law to each component individually in a circuit.

Formal View

Ohm's law for a linear (ohmic) conductor is V = IR, where R is constant. In differential form, \vec{J} = \sigma \vec{E}, where \vec{J} is current density and \sigma = 1/\rho is the conductivity. Ohm's law is an empirical relation, not a fundamental law of physics.

🚧 Common Stuck Point

Ohm's law applies to individual components, not always to the whole circuit at once.

⚠️ Common Mistakes

  • Applying Ohm's law to the entire circuit when resistors are in parallel — Ohm's law relates the voltage across a single component to the current through that component; use equivalent resistance for the full circuit.
  • Thinking Ohm's law applies to all materials — it only holds for ohmic conductors (like metals at constant temperature); diodes, LEDs, and filament bulbs are non-ohmic.
  • Using milliamps or kilohms without converting — all values must be in base units (amps, volts, ohms) before substituting into V = IR.

Common Mistakes Guides

Electric Current

Frequently Asked Questions

What is Ohm's Law in Physics?

The fundamental relationship stating that the voltage (V) across an ohmic conductor equals the current (I) flowing through it multiplied by its resistance (R).

What is the Ohm's Law formula?

V = IR or equivalently I = \frac{V}{R} or R = \frac{V}{I}

When do you use Ohm's Law?

When solving an Ohm's law problem, first identify the component you are analysing and determine which two of the three quantities (V, I, R) you know. Then rearrange the formula to solve for the unknown: V = IR, I = V/R, or R = V/I. Apply the law to each component individually in a circuit.

How Ohm's Law Connects to Other Ideas

To understand ohm's law, you should first be comfortable with voltage, resistance and electric current. Once you have a solid grasp of ohm's law, you can move on to series circuit, parallel circuit and electrical power.

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