Question

a cylindrical conductor has a resistance of 18 ohms . it is cut into three equal parts. if the three parts are connected in parallel,the effective resistance of the combination is

Answer 1

R = 1/R1 +1/R2+1/R3

= 1/6 + 1/6 + 1/6

= 3/6

= 1/2

= 0.5 ohm

Answer 2

The effective resistance of the combination is 0.5 ohms.

Given,

Resistance of cylindrical conductor, R = 18 Ω

To Find,

The effective resistance, when the cylindrical conductor is divided into three equal parts and these parts are connected in parallel

Solution,

We have been given the resistance of a cylindrical conductor, R = 18 Ω

Now, if this conductor is divided into three equal parts with resistances R1, R2, and R3, then the resistance of each of these parts would be equal.

⇒ R1 = R2 = R3 = R/3

⇒ R1 = R2 = R3 = 18/3

⇒ R1 = R2 = R3 = 6

Also, given the three equal parts of this conductor is connected in parallel. Therefore, effective resistance R' is given by:

R' = 1/R1 + 1/R2 + 1/R3

⇒ R' = 1/6 + 1/6 + 1/6

⇒ R' = 3/6

⇒ R' = 0.5 Ω

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