Electrical Resistance

When electric current flows through a conductor, the conductor opposes the orderly motion of the charge carriers. This property of a conductor is called electrical resistance.

For the same potential difference, a conductor with greater resistance carries less current, while one with smaller resistance carries more current. From Ohm's law—

The SI unit of resistance is ohm (Ω).

👉 Factors Affecting Resistance

The resistance of a conductor mainly depends on four factors—

⭐ the material of the conductor

⭐ its temperature

⭐ its length

⭐ its cross-sectional area

⭐ Effect of Material

Two wires having the same length, the same cross-sectional area, and the same temperature can have different resistances if they are made of different materials. For example, silver has a lower resistivity than iron, so under the same conditions a silver wire is a better conductor than an iron wire.

⭐ Effect of Temperature

• For most pure metals, resistance increases as temperature increases.
• In materials such as carbon, silicon, germanium, and electrolytes, resistance may decrease as temperature increases.
• In some alloys such as invar, manganin, and constantan, resistance changes comparatively little with temperature.

⭐ Relation Between Resistance and Length

When material, temperature, and cross-sectional area remain constant, the resistance of a conductor is directly proportional to its length.

Therefore, increasing the length of a wire increases its resistance, while decreasing its length reduces the resistance.

⭐ Relation Between Resistance and Cross-sectional Area

When material, temperature, and length remain constant, resistance is inversely proportional to the cross-sectional area.

A thick wire has a larger cross-sectional area and therefore a lower resistance than a thin wire of the same material and length.

Combining equations (i) and (ii)—

Therefore,

For a given material at a fixed temperature, ρ is a constant. It is called the resistivity of the material.

👉 Resistivity

For a particular material at a fixed temperature, is a characteristic physical quantity. From the resistance formula—

Resistivity is related to the resistance of a specimen having unit length and unit cross-sectional area, but unlike resistance, it is a property of the material itself at a specified temperature.

SI Unit

Therefore, the SI unit of resistivity is ohm metre (Ω·m).

Difference Between Resistance and Resistivity

👉 Why Does Stretching a Wire Change Its Resistance?

A metallic wire has a resistance of 6 Ω. It is stretched so that its length becomes twice the original length. Assume that its volume remains unchanged.

Initially,

The new length is—

Since volume remains constant,

Therefore,

Hence,

Answer: 24 Ω

👉 Conductance

The easier it is for a conductor to allow electric current to pass through it, the greater its conductance. Conductance is the reciprocal of resistance.

Its SI unit is siemens (S).

👉 Conductivity

Conductivity is the reciprocal of resistivity.

Its SI unit is—

A material with lower resistivity generally has higher conductivity.

👉 Semiconductor and Superconductor: A Brief Introduction

📚 Semiconductor

A material whose electrical behaviour lies between that of a good conductor and an insulator is called a semiconductor. Silicon (Si) and germanium (Ge) are common examples. Their resistance may decrease as temperature increases.

📚 Superconductor

When certain materials are cooled below a characteristic critical temperature, their electrical resistance becomes zero in the superconducting state. This phenomenon is called superconductivity. Examples include mercury below about 4.2 K and lead below about 7.2 K.

These are introductory ideas; superconductivity is studied in greater detail at higher levels.

📚 Effects of Light, Magnetic Field, and Pressure on Resistance

⭐ The resistance of selenium can decrease when light falls on it, and greater light intensity may reduce the resistance further.

⭐ The resistance of bismuth can change when it is placed in a magnetic field.

⭐ In some materials, resistance changes with pressure. The resistance of carbon granules changes when pressure changes, a property historically used in carbon microphones.

These points are additional information beyond the core Class 10 resistance formulas.

📚 Use of a Rheostat to Control Resistance

⭐ A rheostat is used to increase or decrease the effective resistance in a circuit as required. According to Ohm's law, changing the resistance changes the current when the applied potential difference is fixed.

⭐ Variable resistance has also been used in regulators and other electrical control devices to control current.

📚 General Properties Desired in Resistance Materials

⭐ Resistance should not change too much with temperature when stability is required.

⭐ Resistance should be affected as little as possible by humidity.

⭐ The material should have a suitable, often relatively high, resistivity for the intended application.

⭐ It should be able to withstand the heat produced during operation.

✏️ Example 1

Two wires of the same material have equal lengths. The radius of the first wire is twice the radius of the second. Find the ratio of their resistances.

The radius of the first wire is and that of the second is .

Answer: 1 : 4

✏️ Example 2

Two wires are made of the same metal. The first wire has a resistance of 10 Ω. The second wire is three times as long and has half the cross-sectional area of the first. Find the resistance of the second wire.

Answer: 60 Ω

✏️ Example 3

A wire is 25 cm long and has a cross-sectional area of 0.15 cm². When a potential difference of 5 V is applied across it, a current of 2 A flows. Find the resistivity.

First,

Then,

✍ Try It Yourself

🔹 Two wires of the same material have lengths in the ratio 2:3 and equal cross-sectional areas. Find the ratio of their resistances.

🔹 If the length of a wire is doubled while its cross-sectional area remains unchanged, how does its resistance change?

🔹 If the cross-sectional area of a wire is doubled while its length remains unchanged, by what factor does its resistance change?

🔹 If , , and , calculate the resistivity.