Question

A cable has two conductors, which are connected together at one end of the cable for testing purposes. When the cable is 700 m long, the resistance of the connected loop is found to be 100 Ω when measuring from the other end. The value of resistance of 8 km long same cable is _______.
1. 1,100 Ω
2. 1,134 Ω
3. 1,200 Ω
4. 1,143 Ω

Answer 1

Correct Answer - Option 4 : 1,143 Ω

Concept:

Resistance: The property by which an electric conductor opposes the flow of current through it is called the resistance of the conductor.

It is denoted by R.

The SI unit of resistance is Ohm (Ω).

\(R = \frac{{ρ \;l}}{A}\)

Where ρ is the resistivity of a conductor, l is the length of the conductor and A is the cross-sectional area.

Calculation:

When the cable is 700 m long, the resistance of the connected loop is found to be 100 Ω.

Let,

l₁ = 700 m
R₁ = 100 Ω

For 8 km long cable,

l₂ = 8 km = 8000 m

From the above concept,

\(R∝ l\)

∴ 100 Ω ∝ 700 m .... (1)

R₂ ∝ 8000 m .... (2)

From equation (1) and (2),

\(\frac{R_2}{100}=\frac{8000}{700}\)

R₂ = 1,143 Ω