Question

1. Determine the value of minimum resistance that can be made using 6 resistors each of 1/4 Ω.

Answer 1

when all are in series i.e. 1/4*6=3/2 the minimum resistance value using the resistors of resistance 1/4

Answer 2

Given

Total resistors =6 each of 1/4 of ohm


If we connect all in series then

Resultant resistance = sum of all resistance

R= r1+r2+r3+r4+r5+r6

R=1/4 +1/4 +1/4 + 1/4 + 1/4 +1/4

R=1 1/2ohm

R=1.5 ohm


If it is in parallel then

1/R = 1/r1 + 1/r2....... +1/r6



$= \frac{1}{ \frac{1}{4} } + \frac{1}{ \frac{1}{4} } + \frac{1}{ \frac{1}{4} } + \frac{1}{ \frac{1}{4} } + \frac{1}{ \frac{1}{4} } + \frac{1}{ \frac{1}{4} }$


=
$\frac{1}{0.25} + \frac{1}{0.25} + \frac{1}{0.25} + \frac{1}{0.25} + \frac{1}{0.25 } + \frac{1}{0.25}$


$= \frac{6}{0.25}$

1/R= 4/1

R=1/4

R=0.25 ohm

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