A steel wire and a copper wire, both possessing equal length and...

Stress is defined as the internal restoring force per unit area.

When the wires are joined end to end and subjected to a tension, they are in a series combination. Therefore, the same force $F$ acts on both the steel and copper wires.

It is given that both wires have the same cross-sectional area $A$.

The stress in the steel wire is $\sigma_{s} = \dfrac{F}{A}$.

The stress in the copper wire is $\sigma_{c} = \dfrac{F}{A}$.

The ratio of the stress developed in the steel wire to that in the copper wire is $\dfrac{\sigma_{s}}{\sigma_{c}} = \dfrac{F/A}{F/A} = 1$.