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Physics Formulas

Electrical Resistance Formula

Electrical resistance is a quantity that measures the opposition offered by a device or a material to the flow of electric current. A resistor is an electric component that is used to offer the desired resistance in a circuit. In this article, we will discuss the concept of electric resistance and various electrical resistance formula with examples. Let us learn the concept!

Electrical Resistance

Concept of Electrical Resistance

To understand its concept let us consider the examples of metallic substances. There are numerous free electrons moving randomly in the crystal structure of a metallic substance. When we apply a voltage across the resistance due to the electric field, then the free electrons drift from lower potential point to higher potential point in the substance.

During this drifting motion, the free electrons continually collide with atoms of the substance. This phenomenon prevents the free motion of electrons and hence this causes resistance.

When some electric voltage is applied across a substance there will be an electric current through it. This applied voltage across the substance is directly proportional to the electric. The constant of proportionality known as the resistance. Therefore resistance is a very important factor for the flow of electric current in an electric circuit. This is based on Ohm’s law.

The unit ohm is normally used for values of resistance. Also for large as well as a very small value of resistance we can use units as giga-ohm, megaohm, kilo-ohm, milli-ohm, micro-ohm even in nano-ohm range depending on the value of resistance.

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The Formula for Electrical Resistance

It can be calculated using Ohm’s law. It is defined as the ratio of the applied voltage to the current. Therefore,

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

Where,

R Electrical Resistance
V Voltage
I Electric current

Also, we can compute the electrical resistance if we know about the material of the object and its geometrical measurements. It is because of the following formula. This formula is using the fact that the value of resistance through a wire will directly proportional to its length and inversely proportional to its cross-sectional area. The formula is,

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

Where,

R Electrical Resistance
\rho The resistivity of the conductor
l The resistivity of the conductor
A The area of the cross-section of the conductor

This formula can also be understood with a water pipe analogy as follows:

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

Solved Examples

Q.1: In an electric circuit, a current of 5.00 A is flowing through a resistor. The voltage drop from one end of the resistor to the other is 100 V. What will be the value of the resistance?

Solution:

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

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

Now, in the above formula, we get

R= \(\frac{100}{5} \)

R = \( 20 \Omega\)

Thus the resistance of the resistor in the circuit will be 20 \( \Omega.\)

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