Question

A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R′, then the ratio R/R′ is _____.

(a) 1/25

(b) 1/5

(c) 5

(d) 25

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Answer 1

Answer:

• Option (D) 25

Explanation:

The resistance is cut into five equal parts, which means that the resistance of each part is R/5.

We know that each part is connected to each other in parallel, hence the equivalent resistance can be calculated as follows:

$\leadsto \sf \: \frac{1}{R'} = \frac{5 }{R} + \frac{5}{R} + \frac{5}{R} + \frac{5}{R} + \frac{5}{R}$

$\leadsto \sf \: \frac{1}{R'} = \frac{5 + 5 + 5 + 5 + 5}{R}$

$\leadsto \sf \: \frac{1}{R'} = \frac{25}{R}$

$\leadsto \sf \: \frac{R}{R'} = 25 \: \: \red \bigstar$

The ratio of R/R′ is 25.

Answer 2

Question :

A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R′, then the ratio R/R′ is _____.

(a) 1/25

(b) 1/5

(c) 5

(d) 25

Given :

• A piece of wire of resistance R is cut into 5 equal parts.
• Then they are connected in parallel.
• Equivalent resistance of parallel combination = R′

To find :

• Ratio of R/R′

Solution :

From the question we can say,

Each part of new combination will be 1/5 of R i.e. R/5

Now we know that,

⇒ 1/R′ = 1/R₁ + 1/R₂ + 1/R₃ + 1/R₄ + 1/R₅ + .........

⇒ 1/R′ = 1/(R/5) + 1/(R/5) + 1/(R/5) + 1/(R/5) + 1/(R/5)

⇒ 1/R′ = 5/R + 5/R + 5/R + 5/R + 5/R

⇒ 1/R′ = 25/R

⇒ R = 25R′

⇒ R/R′ = 25/1

⇒ R/R′ = 25               (Option d)

∴ Ratio R/R′ = 25 . Hence correct answer is option (d)