The given function models the equivalent resistance in ohms, R, when a fixed 9-ohm resistor is connected in parallel with a variable resistor of x ohms.

Question

R
9x
9 + x
Which value of x is closest to the number of ohms needed in the variable resistor for there to be an equivalent resistance, R, of 6.4 ohms?

15.4

57.6

3.7
D
22.2

Answer 1

To find the value of x that results in an equivalent resistance of 6.4 ohms, we set up the equation:

1/R = 1/9 + 1/x

Substitute R = 6.4 and solve for x:

1/6.4 = 1/9 + 1/x
0.15625 = 0.11111 + 1/x
0.04514 = 1/x

x = 1/0.04514
x ≈ 22.2 ohms

Therefore, the closest value of x to achieve an equivalent resistance of 6.4 ohms is 22.2.