# Parallel resistors formula

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The normal textbook formula for resistors in parallel is given as

for two   Rt =(R1*R2)  / (R1+R2)
or
for more     Rt = 1 / (1/R1 +1/R2 + 1/R3  etc..)

I need the formula in the form R1=   and to my shame  I cant remember how to
do the transposition can someone help me out please!
I need a one off resistance of 53.6 ohms (as near as possible) to be made up
from salvage SMT standard values (which seem always slightly under the
nominated) and the Rt =   formula isnt much help!
This resistor  is for an 100x oscilloscope probe and needs to be as small in
size as possible, so two or 3 SMT resistors in parallel would be best.
Thanks

Re: Parallel resistors formula

parallel conductances are much easier.... do that.

write it like this:

1/Rt = 1/R1 + 1/R2

Re: Parallel resistors formula

Already done that - thats easy !
Doesnt get anywhere though - I need R1 = as the formula so I can look
through a range of values leading to the total I need to get to - thought
that was clear!

Re: Parallel resistors formula

Move anything containing R1 to the left and everything else to the
right of the equal sign, switching sign if moved:

1/R1 = 1/R2 - 1/Rt

Now, turn both sides of the equation "upside-down":

R1 = 1/(1/R2 - 1/Rt)

...or if you want to leave the math entirely to someone else, try

Then second hit is
http://www.electronics2000.co.uk/calc/series-parallel-resistor-calculator.php
--
RoRo

Re: Parallel resistors formula

Thanks very much Robert - just what I needed!!  (some basic reminding!! )
and also for the pointer...
Charlie+

Re: Parallel resistors formula

100ohms // 120 ohms // 3300 ohms = 53.65 ohms

a little bit of successive approximation would have easily given you
this answer in less than two minutes.

Re: Parallel resistors formula

And in parallel resistors - the resultant is ALWAYS smaller
than the smallest.

One used to work with slide rules - simple rules were in the mind
to keep the result in bounds.  53 is less than 120 but 530 isn't.
Decimal point goes....

Martin

David Eather wrote:

http://www.electronics2000.co.uk/calc/series-parallel-resistor-calculator.php

Re: Parallel resistors formula

Finger wagging taken!
In the end I used nominally 56 // 1800  which with the value errors taken
into account got me within .05 ohm but I found bunging the formula in a
spreadsheet got me quick answers to any value change!  And the oscilloscope
calibrates spot on with the 100x probe.  I didnt find any 120 SM resistors
on any of my junk boards incidentally.
So thanks to all who gave it some thought and helped.
Charlie+

Re: Parallel resistors formula

Robert Roland wrote:

-1/R1 = 1/R2 - 1/Rt    actually

Although it is easier and less error-prone to subtract 1/R2 from each side.
The procedure is also easier to define in any list of algebraic methods.

--

zero, and remove the last word.

Re: Parallel resistors formula

R1 = - (1/((1/R2) + (1/R3) - (1/Rt)))

Re: Parallel resistors formula

Thanks for your equasion - much easier than the one I home brewed in the
end:  R1=(RtR2R3)/(R2R3)-(RtR3)-(RtR2)
Both got to the correct answers in the application!
Charlie+