Question

if a person has five resistrs each of value 1/5ohm ,then the maximum resistance he can obtain by connecting them is

(1) 5ohm

(2) 1ohm

(3)10ohm

(4)25 ohm​

Answer 1

$\huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}$

Given :

• There are 5 resistors .Each Resistance is of 1/5 ohms

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To Find :

• Maximum Resistance

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Solution :

For minimum value of the resistance add all the resistors in series combination.

$\implies {\sf{R_s \: = \: R_1 \: + \: R_2 \: + \: R_3 \: + \: R_4 \: + \: R_5}} \\ \\ \implies {\sf{R_s \: = \: \dfrac{1}{5} \: + \: \dfrac{1}{5} \: + \: \dfrac{1}{5} \: + \: \dfrac{1}{5} \: + \: \dfrac{1}{5}}} \\ \\ \implies {\sf{R_s \: = \: \dfrac{5}{5}}} \\ \\ \implies {\sf{R_s \: = \: 1}} \\ \\ {\underline{\sf{\therefore \: Maximum \: value \: of \: resistance \: is \: 1 \: \Omega}}}$

Answer 2

$\huge{\underline{\underline{\bf{Solution}}}}$

$\rule{200}{2}$

$\tt given\begin{cases} \sf{There \: are \: 5 \: resistance.} \\ \sf{Value \: of \: each \: resistance \: is \: \frac{1}{5}.} \end{cases}$

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to find the maximum resistance.

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{Explanation :}}}}$

For finding maximum resistance we will put resistor in series.

We know that,

$\Large{\star{\boxed{\rm{R = \frac{1}{R_1} + \frac{1}{R_2} ....... + \frac{1}{R_5}}}}}$

________________[Put Values]

$\tt{→R = \frac{1}{5} + \frac{1}{5} + \frac{1}{5} + \frac{1}{5} + \frac{1}{5}} \\ \\ \bf{Taking \: LCM} \\ \\ \tt{→R = \frac{1 + 1 + 1 + 1 + 1}{5}} \\ \\ \tt{→R = \frac{\cancel 5}{\cancel 5}} \\ \\ \tt{→R = 1} \\ \\ \tt{\therefore \: Maximum \: Resistance \: is \: 1 }$