Question

What is equivalent resistance of three 5 ohm resistors connected in series and parallel?

Answer 1

Answered By Nitul Das

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Answer 2

$\sf \fcolorbox{red}{pink}{ \huge{Solution :)}}$

Given ,

• R1 = 5 ohm
• R2 = 5 ohm
• R3 = 5 ohm

We know that , for series combination

$\sf \fbox{ R_{(s)} = R _{(1)} + R _{(2)} + R _{(3)} }$

Substitute the known values , we get

Total resistance = 5 + 5 + 5

Total resistance = 15 ohm

We know that , for series combination

$\sf \fbox{ \frac{1}{ R_{p} } = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} }$

Substitute the known values , we get

$\sf \mapsto \frac{1}{ R_{p} } = \frac{1}{5} + \frac{1}{5} + \frac{1}{5} \\ \\ \sf \mapsto \frac{1}{ R_{p} } = \frac{1 + 1 + 1}{5} \\ \\ \sf \mapsto \frac{1}{ R_{p} } = \frac{3}{5} \\ \\ \sf \mapsto R_{p} = \frac{5}{3} \\ \\ \sf \mapsto R_{p} = 1.67 ohm$

Hence , the equivalent resistance for series and parallel combination are 15 ohm and 1.67 ohm

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