Physics: Ohm's Law

What is Ohm's Law?

Ohm's Law describes the relationship between voltage, current, and resistance in an electrical circuit.

The law states that the current flowing through a conductor is directly proportional to the voltage applied across it and inversely proportional to its resistance.

Ohm's Law is one of the most important principles in electronics, electrical engineering, and physics.

The Ohm's Law Formula

The basic formula is:

\[ V = IR \]

Where:

\(V\) = Voltage (Volts)
\(I\) = Current (Amperes)
\(R\) = Resistance (Ohms)

Rearranging the formula gives:

\[ I = \frac{V}{R} \]

\[ R = \frac{V}{I} \]

Units Used in Ohm's Law

Quantity	Symbol	Unit
Voltage	\(V\)	Volt (V)
Current	\(I\)	Ampere (A)
Resistance	\(R\)	Ohm (\(\Omega\))

Worked Examples

Example 1: Finding Voltage

A circuit has a current of 2 A and a resistance of 5 Ω. Find the voltage.

\[ V = IR \]

\[ V=(2)(5)=10V \]

Answer: 10 V

Example 2: Finding Current

A resistor has a voltage of 24 V and a resistance of 8 Ω. Find the current.

\[ I=\frac{V}{R} =\frac{24}{8} =3A \]

Answer: 3 A

Example 3: Finding Resistance

A circuit has a voltage of 18 V and a current of 3 A. Find the resistance.

\[ R=\frac{V}{I} =\frac{18}{3} =6\Omega \]

Answer: 6 Ω

Relationship Between Variables

Variable Increased	Effect
Voltage	Current increases if resistance remains constant.
Resistance	Current decreases if voltage remains constant.
Current	Voltage increases if resistance remains constant.

Ohm's Law Triangle

Many students remember Ohm's Law using the formula triangle:

Voltage (V) on top

Current (I) Resistance (R)

Cover the variable you need to find and use the remaining relationship.

Practice Problems

Problem 1:
Find the voltage when current is 4 A and resistance is 3 Ω.

\(V=(4)(3)=12V\)

Problem 2:
Find the current when voltage is 20 V and resistance is 5 Ω.

\(I=\frac{20}{5}=4A\)

Problem 3:
Find the resistance when voltage is 30 V and current is 6 A.

\(R=\frac{30}{6}=5\Omega\)

Problem 4:
A circuit has 12 V across a 2 Ω resistor. Find the current.

\(I=\frac{12}{2}=6A\)

Problem 5:
A current of 0.5 A flows through an 18 Ω resistor. Find the voltage.

\(V=(0.5)(18)=9V\)

Challenge Problems

A 9 V battery powers a 3 Ω resistor. Find the current.
A circuit draws 2.5 A from a 15 V source. Find the resistance.
A resistor of 12 Ω carries 0.75 A. Find the voltage.
What happens to current if resistance doubles while voltage remains constant?
Explain why Ohm's Law is useful when designing electrical circuits.