in an electric circuit with a resistance wire and a cell, the current flowing is I. What would happen to this current if the wire is replaced by another thicker wire of same material and same length? give reason

The current will increase.

This will happens because a thicker wire of the same material will have a lower resistance. Now as the resistance is low current flowing in the wire gets lower resistance towards flow from the conductor and hence greater current flows. 

Let the original CSA of the wire be A₁

So R₁ = ρL/A₁

  => ρL = R₁ A₁

Let the CSA of the thicker wire = A₂

A₂>A₁

So R₂ = ρL/A₂

=> ρL = R₂ A₂

Thus,

R₁A₁ = R₂A₂

A₂>A₁

=> R₁> R₂

Now let the potential of the source be V

In First case

V = I₁R₁

In second case

V = I₂R₂

=> I₁R₁ = I₂R₂

Since R₁>R₂

=> I₁ < I₂

Thus current flow in the 2^nd case will be greater.