If R is the total resistance for a parallel circuit with two resistors of resistance r1 and r2, then one over R equals one over r subset one plus one over r subset two . 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

(1 point)
Responses

16 ohms
16 ohms

1,405 ohms
1,405 ohms

27 ohms
27 ohms

102 ohms
102 ohms

Answer 1

To find the resistance, r1, we can use the formula:

1/R = 1/r1 + 1/r2

Plugging in the values:

1/20 = 1/r1 + 1/75
1/20 = (75 + r1)/(75r1)
20r1 = 75 + r1
19r1 = 75
r1 = 75/19
r1 ≈ 3.947

Rounded to the nearest ohm, r1 is approximately 4 ohms. Therefore, the correct answer is not in the options provided.