Question

7:
. A conductor of uniform cross-section, its length 20 m and its resistance 108 Another
conductor of the same material its length 5 m, and of cross-sectional area equals three
times the cross-sectional area of the first. The resistance of the second conductor equals:
a. 9
b. 27
c. 84 ​

Answer 1

Answer:

b) 27

Hope this answer is helpful

Answer 2

Answer:

Option a : 9 Ω

Explanation:

Given:

• Length of the first conductor = 20 m
• Resistance of the first conductor = 108 Ω
• Length of the second conductor = 5 m
• Area of cross section of second conductor = 3 times area of cross section of the first.

To Find:

• Resistance of the second conductor

Solution:

Let the area of cross section and resistivity of the first conductor be A and ρ respectively.

We know that resistance is given by,

R = ρ L/A

where R = resistance

           ρ = resistivity

           l = length

           A = area of cross section

Substituting the values for the first conductor,

108 = ρ × 20/A

ρ/A = 108/20

ρ/A = 5.4 -------(1)

By given we know that area of second conductor is 3 times the area of the first one.

Hence,

Area of second conductor = 3 A

Substituting the values of second conductor,

R₂ = ρ × 5/(3 A)

R₂ × 3 = ρ × 5/A

ρ/A = R₂ × 3/5-------(2)

From equation 1 and 2 LHS are equal, hence RHS must also be equal.

R₂ × 3/5 = 5.4

R₂ × 3 = 27

R₂ = 27/3

R₂ = 9

Hence resistance of the second conductor is 9 Ω.

Hence option a is correct.

Notes:

The resistance of a conductor is directly proportional to it's length. When length increases, resistance increases and vice versa.

The resistance of a conductor is inversely proportional to it's area of cross section. When area increases, resistance decreases and vice versa.

R = ρ L/A