Question

tn an electric circuit with a resistance wire and a cell the current flowing is 'I' . what would happen if the wire is replaced by another thicker wire of same material and same length ? justify your answer

Answer 1

Answer: The resistance would decrease as compared to previous wire as A is inversely proportianl to R.

Let us give some values to understand this question better:

Lets say that the cell has voltage of 2V and the wire is copper of certain area of cross section A and length L and resistance R. There is 1A current flowing through the circuit. the value of ρ remains same as we take only copper wire.

Therefore the resistance R is V/I = 2/1 = 2Ω

Thus 2Ω = ρL/A -------------------(1)

Now if a copper wire which of same length and twice as thick as the previous one is applied, its area of cross-section becomes 2A

therefore, R'= ρL/2A

                    = R' = 1/2(ρL/A)

                     = R' = 1/2(2Ω) {from (1)}

                thus R' = 1Ω ; thus resistance decreases on increasing thickness.