A certain number of identical resistors, each of resistance 5 , are first connected in series and then connected in parallel. If the difference between the effective resistances in the two configurations is 24 , what is the total number of resistors?

Step-by-step solution

Let there be n identical resistors, each of resistance R = 5 . The equivalent resistance in series combination is R_ s = nR = 5n . The equivalent resistance in parallel combination is R_ p = R n = 5 n . Given that R_ s - R_ p = 24 : 5n - 5 n = 24 Multiplying the entire equation by n , we get: 5n² - 24n - 5 = 0 Solving the quadratic equation: 5n² - 25n + n - 5 = 0 5n(n - 5) + 1(n - 5) = 0 (5n + 1)(n - 5) = 0 Since the number of resistors n must be a positive integer, n = 5 . Answer: 5