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