Factors Affecting Resistance: Effect of Material Dimensions

Factors Affecting Resistance: The word Resistance is an important term in electrical terminology. It means opposition to electric current. An electrical circuit has resistance to control to flow of current. It is dependent on certain factors. Let us see what factors affect the resistance in this article.

Resistance Definition

Resistance is defined as the measure of the opposition of a material to the flow of electric current through it. In electronic circuits, a device called a resistor having a fixed resistance is used.

What is Current?

We define current as the rate of flow of charges. When we refer to the movement of charges in electricity, we refer to electrons. The \({\rm{SI}}\) unit for charge is Coulomb, \(Q.\)
\({\rm{current}}\;\left( I \right) = \frac{{{\rm{charge}}\;\left( Q \right)}}{{{\rm{time\;}}\left( t \right)}}\)
\({\rm{SI}}\) unit of current is Ampere, \(A.\) \({\rm{1 A}}\) is the current flowing when \({\rm{1 C}}\) of charge flows in \({\rm{1 s}}\).

Ohm’s Law

It states that the potential difference across a wire is directly proportional to the current flowing through the wire when the temperature of the wire is constant.
\({\rm{V}}\alpha {\rm{I}}\)
The proportionality constant is the resistance, \(R\)
\(V = IR\)

According to Ohm’s law, the potential difference is the product of the resistance of the wire and the current flowing through it.

Unit of Resistance

\({\rm{SI}}\) unit of resistance is Ohm \(\left( \Omega  \right)\),  after Georg Simon Ohm \({\rm{(1784 – 1854)}}\), a German physicist who postulated the law relating voltage, current with resistance.

What are the 4 Factors that Affect Resistance?

All conductors have some resistance. The resistance of the conductor depends on the following factors:
1. Length of the conductor
2. The thickness of the conductor
3. The material it is made of
4. The temperature of the conductor
The resistance is:
1. directly proportional to the length \({\rm{(l)}}\) of the conductor.
2. inversely proportional to the cross-sectional area or thickness \({\rm{(A)}}\) of the conductor.

This means that,
\({\rm{R}} \propto {\rm{l}}\)
\({\rm{R}} \propto \frac{{\rm{1}}}{{\rm{A}}}\)
Therefore,
\({\rm{R}} \propto \frac{{\rm{1}}}{{\rm{A}}}\)
The proportionality constant is called resistivity \((\rho )\) of the material.
The equation relating all these is:
\({\rm{R = }}\frac{{{\rm{\rho l}}}}{{\rm{A}}}\), ohms

Let us go through each of these in detail.

Resistance and Length of Conductor

Resistance is directly proportional to the length of the conductor.
\({\rm{R}} \propto {\rm{l}}\)
Simply put, the longer the conductor, the more its resistance. Therefore, when the current must pass through a long distance in a conductor, it meets higher opposition. The analogy for this in real life is:
1. When the distance between two places is more, we take a longer time to reach than in a shorter distance.
2. Water comes out faster in a shorter pipe than a longer one.

This extra time is equivalent to the resistance met by the moving charges.

Resistance and Cross-sectional Area of a Conductor

Resistance is inversely proportional to the cross-sectional area of the conductor.
\({\rm{R}} \propto \frac{{\rm{1}}}{{\rm{A}}}\)
In simple words, the thicker the conductor, the smaller is its resistance. It means that resistance is high in a thin conductor.
A conductor with more cross-sectional area has more area for the charges to flow. So, they encounter less opposition. We can see the analogies for this in our daily life:
1. It is easier to walk in a wide corridor than a narrow one. However, in a narrow corridor, we bump into people more, hindering our movement. This hindrance is equivalent to the resistance to current.
2. Traffic is smooth with less crowding on a wide road than a narrow lane or a bottleneck.
3. There is more pressure of water in a thin pipe than in a wider pipe.

Resistivity of Materials

Resistivity is a measure of how well a material resists (or opposes) current flowing through it. It is the inherent property of a material to oppose current and is fixed for a particular material.
It is also called specific resistance.
We define resistivity or specific resistance as the resistance offered by a material of one-metre cube dimension. It means that it has a length of \({\rm{1}}\,{\rm{m}}\) and a cross-sectional area of \({\rm{1}}\,{{\rm{m}}^{\rm{2}}}\).
Its unit is ohm-metre \((\Omega {\rm{m}})\)
\({\rm{R = }}\frac{{{\rm{\rho l}}}}{{\rm{A}}}\)
If \({\rm{l = 1}}\) and \({\rm{A = 1\;}}{{\rm{m}}^{\rm{2}}}\), then unit of resistivity is,
\({\rm{\rho  = }}\frac{{{\rm{RA}}}}{{\rm{l}}}{\rm{ = }}\frac{{{\rm{\Omega  \times 1\;}}{{\rm{m}}^{\rm{2}}}}}{{{\rm{1\;m}}}}{\rm{ = \Omega m}}\)
There is another term called conductivity. Conductivity is a measure of how well a material allows current through it. It is the reciprocal of resistivity.

Types Of Electrical Materials

All materials have some amount of resistance, some may be high, and some may be low. Based on the level of opposition a material has for current through it, we classify them as conductors and insulators.

There is a third type of material called a semiconductor. As the name says, these materials conduct partially. Their resistivity is between those of insulators and conductors. They are used in electronic circuits for controlling the current.

The specific resistance of some materials are as below:

Resistance and Temperature

Heat is due to the motion of atoms in a material. The higher the temperature, the more is this movement. Therefore, with high temperature, resistance increases as the electrons collide more with the atoms surrounding them. Therefore, Ohm’s law is applicable with a clause that the temperature is constant.
Dependency of the resistance with the temperature can be written as,
\(R = {R_0}\left( {1 + \alpha \left( {T – {T_0}} \right)} \right)\)
Where,
\(R\) is the resistance when the temperature is \(T\)
\({R_0}\) is the resistance when the temperature is \({T_0}\)
\(\alpha\) is the temperature coefficient of the resistivity
Superconductors are materials that have almost zero resistance. It is made possible by cooling the material to extremely low temperatures.
The reverse effect is that high resistance increases the temperature of the conductor through which current is passing. This property is made use in incandescent bulbs made of the tungsten filament in electric heaters and radiators.

Working Of Tungsten Bulb

We can explain it using the resistance formula,
\(R = \frac{{\rho l}}{A}\)
1. Tungsten is a metal that has a very high melting point, so it does not melt quickly. It has a high specific resistance of \(5.6 \times {10^{ – 8}}\Omega {\rm{m}}\).
2. The filament inside the bulb is extremely thin, meaning a very small cross-sectional area, \(A.\)
3. It is made of coils within coils, thereby lengthening it, making \(l\) very high.

These three factors give rise to very high resistance. The charges cannot move ahead in such high opposition without increasing the temperature. So, the wire becomes so hot that it starts glowing and giving out light.

Factors that Affect Resistance – Sample Problems

Q.1. What is the resistance of a copper wire of length \(5\;{\rm{m}}\), with a cross-sectional area of \(1\;{\rm{m}}{{\rm{m}}^2}\)? The specific resistance of copper is \(1.7 \times {10^{ – 8}}\Omega {\rm{m}}\).
Ans: Given,
The length of the wire \({\rm{l = 5\;m}}\)
Area of the cross-section of the wire \(A = 1\;{\rm{m}}{{\rm{m}}^2} = {10^{ – 6}}\;{{\rm{m}}^2}\)
Resistivity \({\rm{\rho  = 1}}{\rm{.7 \times 1}}{{\rm{0}}^{{\rm{ – 8}}}}{\rm{\Omega m}}\)
We know resistance \(R = \frac{{\rho l}}{A}\)
\(\Rightarrow R = \frac{{1.7 \times {{10}^{ – 8}} \times 5}}{{{{10}^{ – 6}}}} = 0.085\;{\rm{\Omega }}\)

Q.2. What happens to the resistance of a wire if its area is doubled and length is halved?
Ans: Resistance equation is,
\({{\rm{R}}_{\rm{1}}}{\rm{ = }}\frac{{{\rm{\rho }}{{\rm{l}}_{\rm{1}}}}}{{{{\rm{A}}_{\rm{1}}}}}\)
and
\({{\rm{R}}_{\rm{2}}}{\rm{ = }}\frac{{{\rm{\rho }}{{\rm{l}}_{\rm{2}}}}}{{{{\rm{A}}_{\rm{2}}}}}\)
Therefore,
\(\frac{{{{\rm{R}}_{\rm{2}}}}}{{{{\rm{R}}_{\rm{1}}}}}{\rm{ = }}\frac{{{{\rm{l}}_{\rm{2}}}}}{{{{\rm{l}}_{\rm{1}}}}}{\rm{ \times }}\frac{{{{\rm{A}}_{\rm{1}}}}}{{{{\rm{A}}_{\rm{2}}}}}\)
\({{\rm{l}}_{\rm{2}}}{\rm{ = 0}}{\rm{.5 \times }}{{\rm{l}}_{\rm{1}}}\)
\({{\rm{A}}_{\rm{2}}}{\rm{ = 2 \times }}{{\rm{A}}_{\rm{1}}}\)
\(\frac{{{{\rm{R}}_{\rm{2}}}}}{{{{\rm{R}}_{\rm{1}}}}}{\rm{ = }}\frac{{{{\rm{l}}_{\rm{2}}}}}{{{{\rm{l}}_{\rm{1}}}}}{\rm{ \times }}\frac{{{{\rm{A}}_{\rm{1}}}}}{{{{\rm{A}}_{\rm{2}}}}}{\rm{ = 0}}{\rm{.5 \times 0}}{\rm{.5 = 0}}{\rm{.25}}\)

The material’s resistance is reduced to \(25\% \) of the original resistance when the length is halved and the area is doubled.

FAQs On Factors Affecting Resistance

Q.1. Why does a short circuit causes fire?
Ans: When two current-carrying conductors get connected accidentally, there is very low resistance there. So more current starts flowing. The wire is not able to handle this high current. So, the temperature rises, causing the insulating cover around it to melt and start burning. This causes a fire.

Q.2. Why do we wear rubber slippers and gloves when working with electricity?
Ans: Rubber is an insulator and does not allow current to flow through it. It has a very high resistance. So, we are protected from electric shock when we use rubber and plastic materials.

Q.3. The electric cables that carry current are made of thick bundles of wires. Why?
Ans: Higher the cross-sectional area, the lower is the resistance.

Q.4. Why are superconductors kept at a very low temperature?
Ans: Heat increases the resistance. So, superconductors are kept at a very low temperature to make the resistance almost zero.

Q.5. Why are the leads in electronic circuits very short?
Ans: Resistance increases with the length of the wire. Therefore, resistance must be kept low to increase the value of current. So, the lead wires are made to be as short as possible.

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