This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Determine the relationship between r, R, and n for the parallel connection. When n resistors, each of resistance r , are connected in parallel, the equivalent resistance R is given by the formula: (1)/(R) = (1)/(r) + (1)/(r) + + (1)/(r) (n times) (1)/(R) = (n)/(r) From this equation, we can express r in terms of R and n: r = nR Step 2: Calculate the equivalent resistance if the resistors were connected in series. If the same n resistors, each of resistance r , were connected in series, the equivalent resistance R_series would be: R_series = r + r + + r (n times) R_series = n × r Step 3: Substitute the value of r from Step 1 into the series resistance formula. Substitute r = nR into the equation for R_series: R_series = n × (nR) R_series = n^2 R The equivalent resistance of the combination if connected in series would be n^2R. Comparing this with the given options: [A] n^2R [B] R/n^2 [C] R/n [D] nR The calculated resistance matches option [A]. The final answer is A. That's 2 down. 3 left today — send the next one.