# The insulation resistance of a cable of length 10 km is 1 MΩ. its resistance for 50 km length will be

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The insulation resistance of a cable of length 10 km is 1 MΩ. its resistance for 50 km length will be
1. 1 MΩ
2. 5 MΩ
3. 0.2 MΩ
4. 2 MΩ

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Correct Answer - Option 3 : 0.2 MΩ

Concept:

Insulation resistance is inversely proportional to length of the cable

$R = \frac{\rho }{{2\pi l}}\log \frac{{{r_2}}}{{{r_1}}}$

$\Rightarrow R \propto \frac{1}{l}$

where,

r= radius of cable, r1 = radius of core conductor, l = length of cable

Calculation:

Given

l1 = 10 km, R1 = 1 MΩ, l2 = 50 km

$\Rightarrow \frac{{{R_1}}}{{{R_2}}} = \frac{{{l_2}}}{{{l_1}}}$

$\Rightarrow \frac{{1 }}{{{R_2}}} = \frac{50}{10} \Rightarrow {R_2} = 0.2\;M{\rm{Ω }}$