Question

Hello Users!

Judge the equivalent resistance when the following are connected in parallel-

(a) 1Ω and 106Ω
(b) 1Ω and 103Ω and 106Ω.

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Answer 1

(a) When 1 Ohm and 106 ohm are connected in parallel.

$\frac{1}{ r_{p} } = \frac{1}{1} + \frac{1}{106} \\ \\ \frac{1}{ r_{p} } = \frac{106 + 1}{106} \\ \\ r_{p} = \frac{106}{107} ohm$


(b) When 1 Ohm , 103 ohm and 106 ohm are connected in parallel.

$\frac{1}{ r_{p} } = \frac{1}{1} + \frac{1}{103} + \frac{1}{106} \\ \\ \frac{1}{ r_{p} } = \frac{103 \times 106 + 106 + 103}{103 \times 106} \\ \\ \frac{1}{ r_{p} } = \frac{10918 + 106 + 103}{10918} \\ \\ \frac{1}{ r_{p} } = \frac{11127}{10918} \\ \\ r_{p} = 1.01ohm$