Final answer:
The original resistance of the wire is 4.50 x 10⁻⁸ ohms. After cutting it into four pieces and connecting them side by side, the new resistance is 1.125 x 10⁻⁸ ohms.
Step-by-step explanation:
To solve the mathematical problem completely, we need to understand the relationship between the resistance (R) of a wire, its length (L), and its cross-sectional area (A). According to the formula R = ρ(L/A), where ρ is the resistivity of the material, resistance is proportional to the length of the wire and inversely proportional to its cross-sectional area.
When a wire of resistance 4.50 x 10⁻⁸ ohms is cut into four equal pieces, each piece will have the original length divided by four and the same cross-sectional area. If these four pieces are connected side by side (parallel), the combined cross-sectional area becomes four times larger because area is additive in parallel. Since the resistance of each piece is the same, the total resistance of the wire when connected in parallel is the original resistance divided by four.
Thus, the new resistance of the wire can be calculated by dividing the original resistance by four: R_new = (4.50 x 10⁻⁸ Ω) / 4 = 1.125 x 10⁻⁸ ohms. This is the resistance of the new wire arrangement when the original wire is cut into four pieces and connected side by side