Electrical Resistance Formula, Calculation of Ohms

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Electrical Resistance Formula

A large number of free electrons move randomly in the crystal structure of a metallic material. When a voltage is applied across a resistance due to an electric field, the free electrons move from a point of low potential to a point of high potential in the material.

During this drifting motion, the free electrons continuously collide with the atoms of the material. This phenomenon prevents the free movement of electrons and hence it causes resistance.

When some voltage is applied to an object there is an electric current through it. This voltage applied to the object is directly proportional to the current.

A constant of proportionality called resistance. So resistance is a very important factor in the flow of current in a circuit. It is based on Ohm’s law.It is represented by R and its SI unit is Ohm Ω (Greeks letter Omega)

Electrical Resistance Formula is given by,

Resistance R(Ω) in ohms is equal to the product of the resistivity of the conductor ρ(Ω.m) in ohm meter is multiply by Length L(m) in meter is divided by the cross-sectional area of the conductor A.Hence the electrical resistance formula has been written as,

R(Ω) = ρ(Ω.m) L(m) / A

Where,
ρ is the resistivity of the conductor in Ω.m

R is the Resistance in Ω

L is the Length in m

A is the cross-sectional area of the conductor.

The constant of proportionality called Resistance R(Ω) in ohm is equal to the product of the V(v) in volts is divided by current through the conductor I(A) in Ampere.Hence the electrical resistance formula has been written as,

R(Ω) = V(v) / I(A)

where,

V is the potential difference across the conductor (in Volts),

I is the current through the conductor (in Amperes) and

R is the constant of proportionality called Resistance (in Ohms).

Sample Problems

Example 1

In an electric circuit, a current of 4 A is flowing through a resistor. The voltage drop from one end of the resistor to the other is 12 V. What is the value of the resistance?

Solution 

According to the relation:

V = IR

or

R = V/I

Therefore,

R = 12 V/4 A

R= 3 Ω.

Example 2

What is the current flowing through the circuit in which applied voltage is 12 V and resistance of the conductor is 3 ohms?

Solution 

According to the relation:

V = IR

or

I = V/R

This implies,

I = 12 V/3 Ω

I = 4 A.

 

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