Question

If R is the total resistance of two resistors connected in parallel with resistances R1 and R2, then R=R1R2/(R1+R2). If R1 is measured to be 16 ohms with a possible percentage error of 3 percent while R2 is measured to be 34 ohms with a possible percentage error of 5 percent, use differentials to estimate the maximum percentage error in the calculation of R.

Answer 1

\[dR ={ {\partial R} \ \over { \partial R_1}} dR_1 + { {\partial R} \ \over { \partial R_2}} dR_2\]

So you need to calculate this and the substitute into the RHS.

Answer 2

ya i did that but it say wrong answer

Answer 3

i found dr/dr1 =r^2/(r1+r2)^2

Answer 4

dR/dR1 (partials) = [ (R1 + R2)R2 - R1R2 ] / (R1 + R2)^2
= R2^2 / (R1 + R2)^2

Answer 5

ya its the same i got but im getting wrong answer ?

Answer 6

you wrote down above r^2/(r1 + r2)^2;
did you calculate with r2^2 in the numerator?

Answer 7

R1 =16
R2=34
dr1 0.03
dr2=0.05

Answer 8

ya i did r2^2

Answer 9

ah dr1 is not 0.03. It is 3% of R1. So dr1 = 0.03 x 16 = 0.48

Answer 10

same for dr2

Answer 11

ok i got it so i ll put dr2=1.7 right?

Answer 12

yes

Answer 13

do i need to *100 the ansewr to get % error

Answer 14

the % error of a variable X is dX/X

Answer 15

u know im getting wrong anserw too

Answer 16

i got 0.3960

Answer 17

and it say wrong ?????????????

Answer 18

that's far too high. There can't be 39.6% error. You've made a calculation error somewhere along the way.

Answer 19

(dX/X * 100 is the % error, strictly speaking)

Answer 20

im doing it again and still same number

Answer 21

0.396

Answer 22

can u tell me where im wrong ???????????

Answer 23

I get 7.7%

Answer 24

coeff R1 = r1^2/(r1+r2)^2

and r1 error = (coeff r1)*(delta r1)

Answer 25

ya but i didnt get my coeff r1 is ur coeff r2

Answer 26

and ur answer is wrong too

Answer 27

Oh, yes, I reveresed it. One sec

Answer 28

the error is not delta R

Answer 29

which u got .396 same as mine ?

Answer 30

No. We want dR/R * 100. That's the percentage error

Answer 31

so how u got r

Answer 32

We have the same dR, which is good. But that's not percentage error. That's absolute error.

Answer 33

I calculated it using the original formula!

Answer 34

ok which is 10.88

Answer 35

Yep

Answer 36

i got 3.639 %

Answer 37

Yes, as did I: delta R/R

Answer 38

and it is correct :)

Answer 39

good

Answer 40

thanks :)