Final answer:
The internal resistance to a change in shape under external force in a metal is its resistivity. This property is intrinsic to the material and affects both its resistance to electrical current and deformation. Resistance also varies depending on the path of the current through a material, with different paths creating different resistance values.
Step-by-step explanation:
The internal resistance to a change in shape when an external load or force is applied to a metal is known as its resistivity. Resistivity is the property of a material that offers resistance to the flow of charge and thus to the deformation under external force.
It is an intrinsic property of a material that is independent of its shape or size. Deformation of a material under force includes various behaviors such as squashing, twisting, or pulling, which all relate to the concepts of stress and strain in the physical sciences.
In a physics context, for a cylindrical object like a wire, the electrical resistance R is directly proportional to its length L and inversely proportional to its cross-sectional area A. Moreover, R is directly proportional to the material's resistivity ρ. This means that materials with a higher resistivity will accordingly have a higher resistance to both the flow of electrical current and structural deformation.
The resistance of an object also depends on the path current takes through it. For example, a rectangular bar has different resistance values along its length compared to across its width due to the varying path lengths that affect the number of collisions charges make with atoms.