Electrical Resistance Formula

Electrical resistance is a quantity that measures the opposition offered by a device or a material to the flow of current through it. The S.I unit of resistance is ohms (Ω). A resistor is an electric component that is used to offer the desired resistance in a circuit. In this article, we shall be discussing the various electrical resistance formula used to find out the resistance offered by a conductor to the flow of current.

Formula For Electrical Resistance

When we know the length and the cross-sectional area of a conductor, the electrical resistance of a conductor is the product of the resistivity of the conductor and the conductor’s length divided by the conductor’s cross-sectional area. Mathematically, it is represented as follows:

\(R=\rho \frac{l}{A}\)

where, R is the resistance

\(\rho\) is the resistivity of the conductor

l is the length of the conductor

A is the area of the cross-section of the conductor

From the above formula, it is understood that the resistance is directly proportional to the length of the conductor and inversely proportional to the area of the conductor. This formula can be better understood with a water pipe analogy as follows:

  • When the pipe is longer, the length is bigger and hence the resistance to the flow of water is high.
  • When the pipe is wider, the area of the pipe is bigger and hence the resistance to the flow of water is low.

Calculation of Resistance Using Ohm’s Law

The electrical resistance of a conductor can be calculated with Ohms law when the current and the voltage drop across it is known. The formula to calculate the resistance using Ohm’s Law is given as follows:

\(R=\frac{V}{I}\)

where R is the resistance of the resistor R in ohms (Ω),

V is the voltage drop in the resistor in volts

I is the current flowing through the resistor (A)

Electrical Resistance Problems

  1. In an electric circuit, a current of 6.00 A is flowing through a resistor. The voltage drop from one end of the resistor to the other is 150 V. What is the value of the resistance?

Solution:

Here, we know the current and the voltage drop across the conductor hence we can use the Ohm’s law to find the resistance as follows:

\(R=\frac{V}{I}\)

Substituting the values in the above equation, we get

\(R=\frac{150\,V}{6\,A}=25\,\Omega\)

The resistance of the resistor in the circuit is \(25\,\Omega\).

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