Final answer:
When a wire with resistance 'r' is cut into four equal parts and connected in parallel, the equivalent resistance becomes 'r'/4. This decrease in resistance is due to the increase in available paths for the electric current.
Step-by-step explanation:
The resistance of a wire is established as 'r', which is then cut into four equal parts. These parts are then connected in parallel. In a parallel circuit, the total or equivalent resistance (Req) is given by the equation 1/Req = 1/R1 + 1/R2 + 1/R3 + 1/R4. Since each piece of wire is the same, their resistances are equal (r/4), and the equation becomes 1/Req= 4/(r/4).
Therefore, the equivalent resistance in such a setup will be 'r'/4. The key thing to remember is that when resistors are connected in parallel, the total resistance decreases. This is because the electric current has more paths to follow.
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