Question

What is the minimum and maximum resistance can be obtained by using the identical resistor of resistance of (1/5) Ω.​

Answer 1

☯ Minimum Resistance : 0.04Ω

☯ Maximum Resistance: 1Ω

Answer

• We have Five resistors of ⅕ Ω each
• Maximum Resistance = ?
• Minimum Resistance = ?

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• We know that we can obtain the maximum resistance when they are connected in series and the minimum resistance when they are connected in parallel

$\displaystyle\underline{\bigstar\:\textsf{Minimum Resistance :}}$

$\sf\dashrightarrow \dfrac{1}{R_{eq}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}.... + \dfrac{1}{R_n}$

$\sf\dashrightarrow \dfrac{1}{R_{eq}} = \bigg\lgroup\dfrac{1}{1/5}+\dfrac{1}{1/5}+\dfrac{1}{1/5}+\dfrac{1}{1/5}+\dfrac{1}{1/5}\bigg\rgroup$

$\sf\dashrightarrow \dfrac{1}{R_{eq}} = \bigg\lgroup\dfrac{5}{1}+\dfrac{5}{1}+\dfrac{5}{1}+\dfrac{5}{1}+\dfrac{5}{1}\bigg\rgroup$

$\sf\dashrightarrow \dfrac{1}{R_{eq}} = \dfrac{25}{1}$

$\sf\dashrightarrow R_{eq} = \dfrac{1}{25}$

$\sf\dashrightarrow\underline{\boxed{\red{\mathfrak{r_{eq} = 0.04 \ \Omega}}}}$

$\displaystyle\underline{\bigstar\:\textsf{Minimum Resistance :}}$

$\sf\dashrightarrow R_{eq} = R_1+R_2+R_3....+R_n$

$\sf\dashrightarrow R_{eq} = \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5}$

$\sf\dashrightarrow R_{eq} = \dfrac{1+1+1+1+1}{5}$

$\sf\dashrightarrow R_{eq} = \dfrac{5}{5}$

$\dashrightarrow \underline{\boxed{\pink{\mathfrak{r_{eq} = 1 \Omega}}}}$