How to Calculate the Resistance Using Ohm's Law

Electricity is a term used to describe the energy produced (to perform work) when electrons are caused to directionally (not randomly) flow from atom to atom. The day-to-day products that we all benefit from, rely on the movement of electrons. This movement of free electrons between atoms is called electrical current. Current is typically designated as I in circuits. Resistance controls how much electricity flows in a circuit.

The purpose of this article is to provide a clear and concise guide on, how to calculate resistance using Ohm's Law. We will cover the basics of Ohm's Law, its significance, and practical applications. By the end, you will have a clear understanding on how resistance, voltage, and current are related.

What is Resistance?

Resistance is the opposition that a substance offers to the flow of electric current. Resistance is like a barrier to the flow of electric current. Materials with high resistance are referred to as insulators, while those with low resistance are known as conductors. In circuits, components with high resistance are called resistors, which regulate the amount of current in a circuit. Resistance is represented by the symbol 'R', and its SI unit is the ohm (Ω).

Voltage (Electric Potential)

Voltage refers to the difference in charge between two points in a circuit. Unlike current, voltage does not flow through anything but signifies the variance in electrical potential energy between two distinct points or wires. It is measured in volts (V), named after Alessandro Volta, who developed the first battery. One volt is defined as the electric field strength needed in a conductor to push one coulomb of charge through a one-ohm resistance in one second.

What is Ohm’s Law?

Ohm’s Law was given by German physicist Georg Simon Ohm. It states the relationship between current, resistance, and voltage across an electrical circuit. This relationship between current, voltage, and resistance was given by famous German scientist Georg Simon Ohm in 1827. The ratio of potential difference between any two points on a conductor to the current flowing between them, is constant, provided the temperature of the conductor does not change.

This relation can be written as:

V/I = R

or

V = IR

or

R = V/I

here,

• R is constant which depends on the properties of the wire (its material and its dimensions). R is called the resistance of the wire known as Resistance.
• V is applied Voltage.
• I is the current flowing through the electrical circuit.

There are three forms of Ohm’s Law:

• I = V/R
• V = IR
• R = V/I

The three forms of Ohm’s law can be used to define the practical units of current, voltage, and resistance:

• 1 ampere = 1 volt / 1 ohm
• 1 volt = 1 ampere × 1 ohm
• 1 ohm = 1 volt / 1 ampere

How to Calculate the Resistance Using Ohm's Law?

Step 1: Identify the known values. There should be at least two values: voltage (V), current (I).

Step 2: Apply the Ohm's law, V/I = R and calculate the value of resistance (R).

Step 3: Calculate the final value to get the result.

Examples of Calculating Resistance Using Ohm's Law

Example 1: An appliance connected to a 60V outlet draws 3.0A of current. What is the resistance within the appliance?

Solution:

Step 1: Identify the current (I) and voltage (V) that is present in the circuit.

The current within the circuit is I=3.0A, and the voltage is V=60V.

Step 2: Using Ohm's Law: V=IR, calculate the resistance (R) in the circuit.

Put the voltage and current into Ohm's Law:

R=V/I

R=60V/3.0A

R=20 V/A = 20 Ω.

The resistance in the circuit is 20 Ω.

Example 2: A material of unknown resistance is plugged into a circuit. 3.5V are applied to the unknown material, and the current flowing through it is measured to be 1mA. What is the resistance of the unknown material?

Solution:

Step 1: Identify the current (1) and voltage (V) that is present in the circuit.

The current within the circuit is I=1×10-3A=0.001, and the voltage is V=3.5V.

Step 2: Using Ohm's Law: V=IR, calculate the resistance (R) in the circuit.

Plug the voltage and current into Ohm's Law:

R=V/I

R=3.5/0.001

R=3500Ω

The resistance of the unknown material is 3500 Ω.

Example 3: Calculate Resistance from circuit where voltage supplied in 6V and the current flowing in the circuit is 3 A.

Solution:

According to the circuit given in the question, we have V = 6 and I = 3.

putting these values in Ohm's Law Formula; R = V/I we get,

R = 6 V/ 3 A

R= 2 Ω

Example 4: What is the resistance of the circuit in which the applied voltage is 12 V and the current flowing through it is 4 A?

Solution:

Given that,

V = 12 V

I = 4 A

According to the relation

R = V/I

Therefore,

R = 12 V/4 A

R = 3 Ω

Thus, the electrical resistance of the circuit is 3 Ω.

Also, Check

• Resistivity Formula
• Series Circuit Formula
• Limitations of Ohm's Law

Practice Questions

1. If a circuit has a voltage of 12 volts and a current of 3 amps, what is the resistance?

2. A resistor in a circuit has a resistance of 50 ohms. If the voltage across the resistor is 10 volts, what is the current flowing through it?

3. If the resistance in a circuit is 100 ohms and the current flowing through it is 0.5 amps, what is the voltage across the resistor?

4. A circuit has a resistance of 25 ohms and a voltage of 50 volts. What is the current flowing through the circuit?

5. Calculate the resistance of a device if it has a voltage of 24 volts across it and a current of 3 amps flowing through it.