Question

A \(10\ \text{km}\) long cable has an insulation resistance of \(2\ \text{M}\Omega\). What will be the insulation resistance for a \(50\ \text{km}\) length of the same cable?

• A. \(10\ \text{M}\Omega\)
• B. \(0.4\ \text{M}\Omega\)
• C. \(0.2\ \text{M}\Omega\)
• D. \(1\ \text{M}\Omega\)

Hint:

Insulation resistance of a cable decreases as cable length increases.

Answer 1

The Correct Option is B

Concept: Insulation resistance of a cable is inversely proportional to its length: \[ R\propto \frac{1}{L} \]

Step 1: Given: \[ R_1=2\ \text{M}\Omega \] \[ L_1=10\ \text{km} \] \[ L_2=50\ \text{km} \]

Step 2: Since: \[ R\propto \frac{1}{L} \] we use: \[ R_2=R_1\frac{L_1}{L_2} \]

Step 3: Substitute values. \[ R_2=2\times\frac{10}{50} \] \[ R_2=2\times\frac{1}{5} \] \[ R_2=0.4\ \text{M}\Omega \] Therefore: \[ \boxed{0.4\ \text{M}\Omega} \]