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' the ratio R/R' is​

Answer 1

Answer:

The ratio of R/R' is 25.

Answer 2

Answer:

• The ratio R/R' is 25 : 1.

Explanation:

Given that:

• A piece of wire of resistance R is cut into five equal parts.
• These parts are then connected in parallel.
• The equivalent resistance of this combination is R'.

To Find:

• The ratio R/R'.

We know that:

In parallel combination.

• R' = 1/R₁ + 1/R₂ + 1/R₃ + 1/R₄ + ...

Where,

• R' = Equivalent resistance
• 1/R₁, 1/R₂, 1/R₃, 1/R₄ are the resistance at different position.

Finding the equivalent resistance if R is cut into five equal parts:

⇢ 1/R' = 1/(R/5) + 1/(R/5) + 1/(R/5) + 1/(R/5) + 1/(R/5)

⇢ 1/R' = 5/(R/5)

⇢ 1/R' = (5 × 5)/R

⇢ 1/R' = 25/R

⇢ R' = R/25

⇢ R = 25R'

Finding the R/R':

• R : R'
• 25R' : R'

Cancelling R'.

• 25 : 1

Hence,

• The ratio R/R' is 25 : 1.