Question

What is the minimum resistance which can be

made using five resistors each of 1/5 Ω?

Answer 1

 Put them all in parallel- 

(1/R) = (1/(1/5)) + (1/(1/5)) + (1/(1/5)) + (1/(1/5)) + (1/(1/5)) 

= 5 + 5 + 5 + 5 + 5 = 25 

R = 1/25 ohms 

Answer 2

The minimum resistance which can be  made using five resistors is 0.04 ohms.

Explanation:

In parallel combination of resistors, the equivalent resistance is minimum. Equivalent of resistors in parallel combination is given by :

$\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+......$

For 5 resistors each of 1/5 ohms, the equivalent resistance is given by :

$\dfrac{1}{R_{eq}}=\dfrac{1}{(1/5)}+\dfrac{1}{(1/5)}+\dfrac{1}{(1/5)}+\dfrac{1}{(1/5)}+\dfrac{1}{(1/5)}\\\\\dfrac{1}{R_{eq}}=25\\\\R_{eq}=0.04\ \Omega$

So, the minimum resistance which can be  made using five resistors is 0.04 ohms.

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Parallel combination of resistor

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