Answer:
So long as R1 is greater than 2, R will be greater than 1.
Explanation:
Denote the three resistances as R, R1 and R2.
Then:
1 1 1
---- = ------ + -------
R R1 R2
For now, substitute 1 for R and 2 for R2:
1 1 1
---- = ------ + -------
1 R1 2
Solve this for R1. Notice that the LCD here is 2R1.
2R1 = 2 + R1, or R1 = 2. Then we have
1 1 1
---- = ------ + ------- , which, as expected, yields R = 1.
R 2 2
Next, determine the values of R resulting from choices of R1 smaller than 2 and greater than 2:
If R1 = 1.5 (that is, less than 2), then:
1 1 1 2 + 1.5 3.5 3
---- = ------ + ------- = ------------ = -------- . Thus, R = --------- , which is less
R 1.5 2 3 3 3.5 than 1 and
therefore
unacceptable.
Next, let R1 = 2.1 (greater than 1):
1 1 1 2 + 2.1 4.1 4.2
---- = ------ + ------- = ------------ = -------- . Thus, R = --------- , which is greater
R 2.1 2 4.2 4.2 4.1 than 1 and there-
fore acceptable.
Conclusion: So long as R1 is greater than 2, R will be greater than 1.