Electrical Resistance

Electrical Resistance is a barrier caused to the current flow in the circuit. 

While going to any special location with your family, you might have observed when your driver drives the car fastly, on encountering the obstruction on the road, he slows down the car. 

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However, during nights, when it is impossible to see the roads clearly while driving at pace, your car jumps with a high jerk suddenly.

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Do you know what this obstruction is? Well, this obstruction is the resistance, and when this obstruction occurs to the flow of current in an electric circuit, it becomes electrical resistance.

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In this article, we are going to discuss, what is electrical resistance and the factors that affect electrical resistance.

What is Electrical Resistance of a Conductor?

The electrical resistance of a conductor is the obstacle posed by the conductor to the current flowing through it. 

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We define the resistance of a conductor as the ratio of the potential difference ‘V’ applied across the ends of a conductor to the current ‘I’ flowing through its ends. The formula for the electrical resistance is: 

                           R = V/I

(The resistance is symbolized by a letter ‘R’)  

The S.I. unit of the resistance is Ohm, where:

1 Ohm = 1 Volt/ 1 Ampere = 1 V/1A

Thus 1Ω is defined as the resistance of a conductor through which one ampere of current flows through the conductor when a potential difference of 1 V is applied to its ends. 

The dimensional formula for the resistance is: [M1L2T-3A-2].

Factors Affecting Electrical Resistance of Conductor

The resistance of a conducting wire is because of the collision of free electrons in the conductor while drifting towards its positive end.

The resistance of a material viz:  wire, conductor depends on the following factors:

• Length of the material

• Area of the material

• Temperature

• Resistance on Increasing or Decreasing the Length

Consider two identical slabs of conductors each of length ‘l’ and cross-sectional area ‘A’. Let  ‘V’ be the potential difference applied across either of the slabs/conductors and ‘I’ be the current flowing through it.

So, the resistance of the conductor is:

                       R = V/I

Now, placing the two identical conductors side-by-side, the total length becomes l + l = 2l. If the same potential difference is applied across both the slabs, the current becomes I/2. The resistance of the arrangement becomes:

                         R’ = V/I/2 = 2V/I = 2R…..(1)

Equation (1) states that on doubling the length of the wire or any conductor, the resistance also doubles, i.e., R ∝ I.

• Area of the Conductor

Let’s consider a slab and cut it into two halves each of length ‘l’, and a cross-sectional area of ‘A/2’. When the potential difference is applied across the ends of a conductor and the current flowing through it is I/2, then the resistance becomes:

                     R’ = V/I/2  = 2 V/I = 2R…..(2)

Here, we can see from equation (2) that on dividing the conductor slab into two halves, i.e., on halving the area of cross-section of a conductor, the resistance doubles, therefore, R ∝ 1/A.

• Nature of the Material

1. Conductors

Conductors have very low resistance. One must note that copper has very low resistance but its conductance is very high, that’s why copper is used as a connecting wire. While there are other conductors like gold and silver, they also conduct electricity.

If R is the resistance, then conductance ‘G’ is:

                      G = 1/R

2. Insulators

The resistance offered by insulators is very high. In between the conductor and the insulator, there are pure semiconductors, having very high resistance.

3. Alloys

Alloys like Manganin and Constantan offer low resistance, their smaller lengths are required for the wires of a given diameter in making the standard resistances.

• Temperature of the Material

When the temperature of the material increases, the thermal energy of the material also increases because of which ions/atoms of a conductor start vibrating with higher amplitudes and frequencies. 

As the free electrons start drifting towards the positive end of the conductor, the relaxation time reduces. This, in turn, increases the resistance of the conductor. 

If R0 was the resistance of the material at 0℃ and Rf is the current temperature, then the rise in resistance with the rise in the temperature by t℃ is given by:

                           Rf = R0 (1 + ∝t + βt2)

Here, ∝ & β are the temperature coefficients of resistance whose values vary from metal to metal. The unit of 1/K or 1/℃.

In practical applications, is given by:

∝ = \[\frac{R_{f}-R_{0}}{R_{0} \times t}\] = \[\frac{increase \; in \; resistance}{original \; resistamce \times rise \; in \; temparature}\]

So, we define temperature coefficient as the increase in resistance per unit original resistance per degree rise in temperature.

The temperature of is different for different temperatures. Now, if the temperature varies, i.e., if the temperature ranges from t1℃ to t2℃, then ∝ is:

             ∝ = \[\frac{R_{f}-R_{0}}{R_{0} \times (t_{2}-t_{1})}\]