Question

What is the maximum resistance which can be made using five resistors each of 1/5 ohm.
A) 1/5 ohm B)10 ohm
C) 5 ohm D) 1 ohm

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Answer 1

Given that, five resistors and resistance of each of them is 1/5 ohm.

We have to find the maximum resistance which can be made using five resistors each of 1/5 ohm.

R1 = R2 = R3 = R4 = R5 = 1/5 ohm.

Now, there are two ways to find the equivalent resistance. One in series combination and other in parallel combination.

For series:

Rs = R1 + R2 + R3 + R4 + R5

Rs = 1/5 + 1/5 + 1/5 + 1/5 + 1/5

Rs = (1 + 1 + 1 + 1 + 1)/5

Rs = 5/5

Rs = 1 ohm ............(1st equation)

For parallel:

1/Rp = 1/R1 + 1/R2 + 1/R3 + 1/R4 + 1/R5

1/Rp = 1/(1/5) + 1/(1/5) + 1/(1/5) + 1/(1/5) + 1/(1/5)

1/Rp = 5 + 5 + 5 + 5 + 5

1/Rp = 25

Rp = 1/25 ohm ........(2nd equation)

On comparing (1st equation) and (2nd equation) we can say that,

Rs i.e. 1 ohm has the maximum resistance than Rp which can be made using five resistors each of 1/5 ohm.

Option D) 1 ohm

Answer 2

AnswEr:

Option D) 1 Ω

ExplanaTion:

For getting maximum resistance, we should connect the resistors in series combination.

Formula used :

$\large{\boxed{\sf{\red{R_{(s)} = R_{1} + R_{2} + R_{3} + R_{4} + R_{5}}}}}$

Where, resistors are of $\dfrac{1}{5}$ $\Omega$

Putting the values,

$\implies$ $\sf{R_{(s)} = \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5}}$

Taking LCM,

$\implies$ $\sf{R_{(s)} = \dfrac{1+1+1+1+1}{5}}$

$\implies$ $\sf{R_{(s)} = \dfrac{5}{5}}$

$\implies$ $\sf{\blue{R_{(s)} = 1 \Omega}}$

Hence, maximum resistance which can be made using five resistors of $\bold{\dfrac{1}{5}}$ is 1 Ω.