Final answer:
The resistance of a uniform wire bent into a square with each side having a resistance of 9 ohms is determined by recognizing the parallel and series connections; solving this yields the original resistance of the wire as 9 ohms. Option A is the correct answer.
Step-by-step explanation:
The student's question pertains to the resistance of a uniform wire bent into the shape of a square and seeks to determine the resistance of the original wire if the effective resistance across one of its sides is 9 ohms. The resistance of each side of the square can be considered as a resistor in a parallel circuit. Since it's a square, all four resistors (sides of the square) have equal resistance.
To find the total resistance (R) of four resistors of equal resistance (r) when connected in parallel, the formula 1/R = 1/r + 1/r + 1/r + 1/r is used. This equation simplifies to 1/R = 4/r. Given r = 9 ohms as the resistance of one side, we plug the value into the equation to get 1/R = 4/9, or R = 9/4 ohms. However, the total resistance of the wire when shaped into a square will be four times the resistance of a single side because they are connected in series in the shape of a square, so the original resistance of the wire is R total = 4 * (9/4 ohms) = 9 ohms.
Therefore, the correct answer is: (a) 9 ohms.