solve for the variable r only.
thanks.
2006-08-16 15:14:04 · 7 answers · asked by shih rips 6 in Science & Mathematics ➔ Mathematics
Substituting the variables X and Y for r1 and r2 respectively :
1/X + 1/Y = 1/r
r/X + r/y = 1
rX/XY + rY/XY = 1
rX + rY = XY
r(X + Y) = XY
r = XY / (X + Y)
Answer : r = (r1 * r2) / (r1 + r2)
2006-08-16 15:28:44 · answer #1 · answered by Arkangyle 4 · 0⤊ 0⤋
Multiply the two factors of the equation by utilising R(r1)(r2). Upon doing so, you will have r1r2 = Rr2 + Rr1. we would desire to isolate r1, so deliver all r1 words to the comparable facet. r1r2 - Rr1 = Rr2. ingredient out r1, so r1(r2 - R) = Rr2. Now divide by utilising r2 - R r1 = (Rr2)/(r2 - R)
2016-12-17 12:11:53 · answer #2 · answered by Anonymous · 0⤊ 0⤋
THis formula is well-known in the theory of electricity, among other things. The equation can be rewritten as
(r1 * r2) / (r1 + r2)
that is, product divided by sum.
Proof:
1/r = (1/r1) + (1/r2)
Multiply with r1 and r2
(r1 * r2)/r = (r1 * r2)/r1 + (r1 * r2)/r2
(r1 * r2)/r = r2 + r1
Multiply with r
r1 * r2 = r * (r1 + r2)
Now divide by r1 + r2.
2006-08-16 19:54:02 · answer #3 · answered by dutch_prof 4 · 0⤊ 0⤋
This is the formula for resistors in parallel. R=(R1*R2)/(R1+R2)
2006-08-16 16:00:32 · answer #4 · answered by gp4rts 7 · 0⤊ 0⤋
r=1/[(1/r1)+(1/r2)]
2006-08-16 15:19:52 · answer #5 · answered by warelphant 2 · 1⤊ 0⤋
1/r = (r1=r2)/r1r2
r = r1r2/(r1+r2)
2006-08-16 15:23:22 · answer #6 · answered by nirvana 2 · 0⤊ 1⤋
r = 1/((1/r1)+(1/r2)) = (r1*r2)/(r1+r2).
2006-08-16 15:20:50 · answer #7 · answered by mathguy_99 2 · 0⤊ 0⤋