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, substitute the values into the formula:
1/20 = 1/r1 + 1/75
Simplify the equation:
1/20 = (r1 + 75) / (r1 * 75)
Cross multiply to solve for r1:
75 = 20(r1 + 75)
75 = 20r1 + 1500
-1425 = 20r1
r1 = -71.25
Since resistance cannot be negative, we can conclude that the answer is not valid.