You are given one hundred $1 \Omega $ resister. What is the smallest and largest resistance you can make in a circuit using these?
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Given: $n = 100$, $R = 1\ ohm$
For obtaining the smallest resistance, these resistance are connected in parallel:
Equivalent resistance $=\frac{1}{1}+\frac{1}{1}+\frac{1}{1}....100\ \text{times}=\frac{100}{1}$
$R_{eq}$ $=\frac{1}{100}=0.01\ \text{ohm}$
For obtaining the largest resistance, these are connected in series:
Equivalent reisistance $= 1 + 1 + 1 .........100$ Times $= 100$
$R_{eq} = 100 ohm$
For obtaining the smallest resistance, these resistance are connected in parallel:
Equivalent resistance $=\frac{1}{1}+\frac{1}{1}+\frac{1}{1}....100\ \text{times}=\frac{100}{1}$
$R_{eq}$ $=\frac{1}{100}=0.01\ \text{ohm}$
For obtaining the largest resistance, these are connected in series:
Equivalent reisistance $= 1 + 1 + 1 .........100$ Times $= 100$
$R_{eq} = 100 ohm$
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