Current Electricity

JEE Main level, numerical answer, medium

111 of 380

Question 111 of 380

1010 resistors each of resistance 10Ω10Ω can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be________.

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Answer: 100

When all the resistors are connected in series, the total resistance is
Rmax=10R{R}_{max}=10R
⇒Rmax⁡=10×10=100Ω\Rightarrow {R}_{\max }=10\times 10=100\Omega
When all the resistors are connected in parallel, the total resistance is
Rmin=R10{R}_{min}=\dfrac{R}{10}
⇒Rmin⁡=1010=1Ω\Rightarrow {R}_{\min }=\dfrac{10}{10}=1\Omega
Hence, the ratio,
RmaxRmin=100Ω1Ω=100\dfrac{{R}_{max}}{{R}_{min}}=\dfrac{100\Omega }{1\Omega }=100.

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