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

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You are given one hundred 1 Ω 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 resistances are connected in parallel

Equivalent resistance = $$\frac{1}{1}$$ + $$\frac{1}{1}$$ + $$\frac{1}{1}$$.....10 times = $$\frac{100}{1}$$

$$R_{eq} = \frac{1}{100}$$ = 0.01 ohm

For obtaining the largest resistance, these resistances are connected in series.

Equivalent resistance = 1 + 1 + 1.....100 times = 100

$$R_{eq}$$ = 100 ohm

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