Two wires of equal length, one of aluminium and the other of copper have the same resistance. Which of the two wires is lighter? Hence explain why aluminium wires are preferred for overhead power cables. (ρ_Al = 2.63 x 10^-8 Ω m, ρ_Cu = 1.72 x 10^–8 Ω m, Relative density of Al = 2.7, of Cu = 8.9).

Solution

Given, two wires of equal length have the same resistance.
Let,
Resistance of Aluminium wire , R₁= R and,
Length of wire, l₁= l.
Relative density of Al, d₁ =2.7
Resistivity of Al, $ρ_{Al} = 2.63 \times 10^{- 8} Ωm$

Resistance of Copper wire, R₂ = R
Length of Copper wire, l₂ = l
Relative density of Cu, d₂ =8.9
Resistivity of Cu, $ρ_{Cu} = 1.72 \times 10^{- 8} Ω m$

Using the formula for resistance,

For Aluminium wire,

$R_{1} = ρ_{Al} \frac{l_{1}}{A_{1}}$ = $2.63 \times 10^{- 8} \times \frac{l}{A}$ and,

Since, mass = volume x density

mass of Al wire, m₁ = A₁l₁x d₁ = A₁l₁ x 2.7

For Copper wire,

$R_{2} = ρ \frac{l_{2}}{A_{2}} = 1.72 \times 10^{- 8} \times \frac{l_{2}}{A_{2}} and, mass of Cu wire, m_{2} = A_{2} l_{2} \times d_{2} = A_{2} l_{2} \times 8.9$

Copper wire is 2.2 times heavier than the aluminium wire. That is why, Aluminium wires are preferred over Copper wires for overhead power cables.

Some More Questions From Current Electricity Chapter

What conclusion can you draw from the following observations on a resistor made of alloy manganin?

Current A

Voltage V

Current A

Voltage V

0.2

0.4

0.6

0.8

1.0

2.0

3.94

7.87

11.8

15.7

19.7

39.4

3.0

4.0

5.0

6.0

7.0

8.0

59.2

78.8

98.6

118.5

138.2

158.0

Answer the following questions:
A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?

For Daily Free Study Material Join wiredfaculty

Current Electricity

Some More Questions From Current Electricity Chapter

What conclusion can you draw from the following observations on a resistor made of alloy manganin?

Current A

Voltage V

Current A

Voltage V

0.2

0.4

0.6

0.8

1.0

2.0

3.94

7.87

11.8

15.7

19.7

39.4

3.0

4.0

5.0

6.0

7.0

8.0

59.2

78.8

98.6

118.5

138.2

158.0

Answer the following questions:
A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location

For Daily Free Study Material Join wiredfaculty

Current Electricity

Some More Questions From Current Electricity Chapter

What conclusion can you draw from the following observations on a resistor made of alloy manganin? Current A Voltage V Current A Voltage V 0.2 0.4 0.6 0.8 1.0 2.0 3.94 7.87 11.8 15.7 19.7 39.4 3.0 4.0 5.0 6.0 7.0 8.0 59.2 78.8 98.6 118.5 138.2 158.0

Answer the following questions:A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

What conclusion can you draw from the following observations on a resistor made of alloy manganin?

Current A

Voltage V

Current A

Voltage V

0.2

0.4

0.6

0.8

1.0

2.0

3.94

7.87

11.8

15.7

19.7

39.4

3.0

4.0

5.0

6.0

7.0

8.0

59.2

78.8

98.6

118.5

138.2

158.0

Answer the following questions:
A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?