You are given one hundred $1 Ω$ resistors. What is the smallest and largest resistance you can make in a circuit using these?

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Solution

The greatest possible resistance is when the resistors are connected in series.

$R_{s} = 1 + 1 + 1 + . . . 100 t i m e s = 100 Ω$

The least possible resistance is when the resistors are connected in parallel.

$\frac{1}{R_{p}} = \frac{1}{1} + \frac{1}{1} + \frac{1}{1} . . . 100 t i m e s$

$\Rightarrow \frac{1}{R_{p}} = 100$

$∴ R_{p} = 0.01 Ω$

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You are given one hundred 1 Ω resistors. What is the smallest and largest resistance you can make in a circuit using these?

The greatest possible resistance is when the resistors are connected in series. Rs=1+1+1+...100 times=100 Ω The least possible resistance is when the resistors are connected in parallel. 1Rp=11+11+11...100 times ⇒1Rp=100 ∴Rp=0.01 Ω

You are given one hundred $1 Ω$ resistors. What is the smallest and largest resistance you can make in a circuit using these?