Question

Three unequal resistors in parallel are equivalent to a resistance 1 ohm. If two of them are in the ratio 1:2 and if no resistance value is fractional, the largest of three resistance in ohms is

Answer 1

I just need to understand the calculation...

Answer 2

Actually there is no diagram..but i'll tell u the question

Three unequal resistors in parallel are equivalent to a resistance 1 ohm. If two of them are in the ratio 1:2 and if no resistance value is fractional, the largest of three resistance in ohms is

Answer 3

No all are unequal......and total in || combination is 1 ohm

Answer 4

Three resistors are unequal and any two of them are in the ratio of 1:2.

Answer 5

still trying?

Answer 6

lol...yep

Answer 7

I get 2 3 and 6

Answer 8

I am not able to understand this
f R3 = 3 then 1 R = Ω2

Why u assumed R3 = 3?

Answer 9

@aryandecoolest

Answer 10

\[\large R1=\dfrac{2R3}{2R3-3}\]

Since \(R1\) is an integer, \(2R3-3\) must go evenly in \(2R3\), yes ?

Answer 11

also \(R1\) must be positive, so \(\large 1\le 2R3-3\le 2R3\)

Answer 12

that leaves you with only two possible values for R3 : {2, 3} (why ?)

Answer 13

cuz no resistance value is fractional ?!! O.O

Answer 14

2R3 is always even and 2R3-3 is always odd.
so, R1 is integer only if R3/(2R3-3) is integer.
for R3>3 ,2R3-3>R3 so the only solution of R3 is 2 and 3

Answer 15

ryt !

Answer 16

so, R1 is integer only if R3/(2R3-3) is integer.
for R3>3 ,2R3-3>R3 so the only solution of R3 is 2 and 3

y not 4 ?

Answer 17

cuz no resistance value is fractional ?!! O.O

Answer 18

for R3>3 , 2R3-3>R3 which means R3/(2R3-3) will always be fractional
so R3 cannot be greater than 3

Answer 19

see now there's the thing....!! clearly written no value can be fractional...if you solve yourself once and try substituting values you will analyze it. That's the reason i took R3=3 for your question.....you can go other way round...assume value for R2 and solve.

Answer 20

ok...so it's kinda trial and error ?

Answer 21

testing two values is not a trial and error

Answer 22

and since we want the largest resistance we start to check from R3=3 to R3=1.
and since R3=3 gives all the resistance integer.
Largest resistance =2R3 =6 OHM

Answer 23

trial and error would be when you test all infinity numbers hopelessly

Answer 24

aaahhh...i know i am acting like a noob....sorry guys maths is not my forte :(

Answer 25

IN THIS CASE , we dont even need to check for 2 values

Answer 26

Well Thank you guys for the Tremendous Help !

I think i'll take some time to figure it out

Answer 27

np :)

Answer 28

Let the three resistors be y, x and 2x
So
\(\sf \huge 1=\frac{1}{x}+\frac{1}{2x}+\frac{1}{y}\\ \Rightarrow \huge y=\frac{2x}{2x-3}\\ \text{Now x=0 and x=1 is not possible because it will give the value of y as 0 and -2}\\ \text{Any value >3 wil make the denominator>Numerator and thus y will not be integer}\\ \text{So only possible values left are 2 and 3. Since we want the value to be greatest}\\ \text{we take x=3, which give the values 6,3 and 2}\)