Question

a wire whose resistance is 30ohm Is cut into three equal lengths which are then arranged in parallel. Calculate the resistance of the combination

Answer 1

Hi Mate !!


Given resistance of wire is 30ohm

When it is cut into three equal length then the resistance will also get one third as the resistance is directly proportional to the length of the resistor. And all the three resistor have same resistance.


So, the resistance of 1st piece is R/3
2nd piece is R/3
3rd piece is R/3

Hence ,the resistance of all three is R/3 i.e, 30/3 = 10 ohm

• The resistance when they are connected in parallel combination :-

Using the formula to find the resistance in a resistor:-

1/R° = 1/R1 + 1/R2 + 1/R3

Where , R° is the resistance of resistor in parallel combination.

1/R° = 1/10 + 1/10 + 1/10

1/R° = 3/10

R° = 10/3

R° = 3.3 ohm !!

The resistance in the new resistor will be 3.3 ohm !!