If R is the total resistance for a parallel circuit with two resistors of resistance r1 and r2, then 1/R = 1/r_(1) + 1/r_(2). Find the resistance, r1, if the total resistance R is 20 ohms, and r2 is 75 ohms. Round your answer to the nearest ohm if necessary.

Question

A) 16 ohms
B) 1,405 ohms
C) 27 ohms
D) 102 ohms

Answer 1

First, we can use the formula 1/R = 1/r1 + 1/r2 and plug in the values given:

1/20 = 1/r1 + 1/75

Now, let's find a common denominator and simplify:

1/20 = (75 + r1) / (75 * r1)

Now, cross multiply to solve for r1:

r1 = 75 * 20 / (75 - 20) = 1500 / 55 = 27.27 ohms

Rounded to the nearest ohm, r1 is approximately 27 ohms.

Therefore, the answer is C) 27 ohms.