When a wire that has a large diameter and a length L is connected across the terminals of an automobile battery, the current is 40 A . If we cut the wire to half of its original length and connect one piece that has a length L 2 across the terminals of the same battery, the current will be

If we cut the wire to half of its original length and connect one piece that has a length L/2 across the terminals of the same battery, the current will be **twice** of the initial value when the length of wire was L.

Explanation:

V = IR

I = V/R

V = voltage or potential difference across the wire

I = current flowing in the wire

R = Resistance across the length of the wire

But the resistance is a function of the wire's physical attributes like its resistivity (ρ), cross sectional Area (A) and the length of wire (L)

R = ρL/A

If all other parameters are constant, R varies directly as the length of wire if all other parameters are constant

Let all the other parameters be k

R = kL

Initially, the length of the wire is L₁

R₁ = kL₁

I₁ = V/R₁

Then the wire is cut in half

L₂ = L₁/2

R₂ = kL₂

R₂ = kL₁/2 = R₁/2

I₁ = V/R₁

I₂ = V/R₂

Substituting R₂ = R₁/2 into the expression

I₂ = V/(R₁/2) = 2V/R₁ = 2 I₁

This means the current flowing in the wire of length L/2 is twice that flowing in the wire of length L.