GATE 2021 EE – Question 25
Two single-core power cables have total conductor resistances of $0.7\ \Omega$ and $0.5\ \Omega$, respectively, and their insulation resistances (between core and sheath) are $600\ \text{M}\Omega$ and $900\ \text{M}\Omega$, respectively. When the two cables are joined in series, the ratio of insulation resistance to conductor resistance is ________ $\times10^6$.
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Correct answer: 300
Explanation
In series the conductor resistances add, $0.7+0.5=1.2\ \Omega$. The insulation of each cable leaks between core and sheath, so the two insulation resistances are in parallel: $\frac{600\times900}{600+900}=360\ \text{M}\Omega$. The ratio is $\frac{360\times10^6}{1.2}=300\times10^6$.