# Ohm’s Law Statement

Ohm’s law statement: The current flowing through a resistor is directly proportional to the potential difference (voltage) applied across its ends.

Mathematical statement of Ohm’s Law: V = IR

The above two lines explain the original statement of Ohm’s law. We can expand the law to derive the relationship between voltage, current, and resistance.

### Explanation of Ohm’s law statement

For a constant resistance, the amount of current flowing through a circuit is directly proportional to its voltage.

Now, V ∝ R

Let’s consider two cases for a better illustration.

Example # 1: A potential difference of 5 volts is applied to a 10 Ω resistor. Find the current flowing through it.

Solution: From Ohm’s formula, I = V/R = 5 V / 10 Ω = 0.5 A

Example # 2: A potential difference of 10 volts is applied to 10 Ω resistor (Since resistor is constant). Find the current passing through it.

Solution: I = V/R = 10 V / 10 Ω = 1 A

By comparing above cases one can understand that for a constant resistance (10 Ω) the amount of current increases when we increase the voltage.

### Statement for constant voltage

The electrical current flowing through any circuit is inversely proportional to its resistance.

Now, for a constant voltage, statement will become: I = V/R → I ∝ 1/R

The current is inversely proportional to the connected resistor. The two examples below better illustrate the above statement.

Example # 3: A voltage source of 5 V connects to a 10 Ω resistor, find the current flowing through it.

Solution: From formula, I = V/R = 5 V / 10 Ω = 0.5 A.

Example # 4: A voltage source of 5 V connects (Since the source is constant), with a 20 Ω resistance, find the current flowing through it.

Solution: I = 0.25 A.

From above two examples, one can understand that by increasing voltage the current decreases.

### Statement for Constant Current

The amount of voltage dropped across any circuit is directly proportional to its resistance.

Now, V ∝ R

The two cases below better illustrate this,

Example #5: Find the amount of voltage applied across 10 kΩ resistor when a current of 5 mA flows through it.

Solution: V = IR = 5 mA * 10 kΩ = 50 V

Example # 6: Find the amount of voltage applied across the 20 kΩ resistor when a current of 5 mA (since current is constant) flows through it.

Solution: V = IR = 5 mA * 20 kΩ = 100 V.

By comparing both cases one can understand that amount of voltage increases when the resistor increases.