Parallel resistors formula

C

Charlie+

Guest
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
 
On 2009-08-21, Charlie+ <charlie@xxx.net> wrote:
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!
Click to expand...
parallel conductances are much easier.... do that.

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
Click to expand...

write it like this:

1/Rt = 1/R1 + 1/R2
 
On 21 Aug 2009 09:37:05 GMT, Jasen Betts <jasen@xnet.co.nz> wrote as


On 2009-08-21, Charlie+ <charlie@xxx.net> wrote:
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!

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

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


write it like this:

1/Rt = 1/R1 + 1/R2

Already done that - thats easy !
Click to expand...
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!
 
On Fri, 21 Aug 2009 11:11:05 +0100, Charlie+ <charlie@xxx.net> wrote:

1/Rt = 1/R1 + 1/R2

Already done that - thats easy !
Doesnt get anywhere though - I need R1 = as the formula
Click to expand...
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

http://www.google.com/search?q=parallel+resistor+calculator

Then second hit is
http://www.electronics2000.co.uk/calc/series-parallel-resistor-calculator.php
--
RoRo
 
On Fri, 21 Aug 2009 12:48:50 +0200, Robert Roland <fake@ddress.no> wrote as:

On Fri, 21 Aug 2009 11:11:05 +0100, Charlie+ <charlie@xxx.net> wrote:

1/Rt = 1/R1 + 1/R2

Already done that - thats easy !
Doesnt get anywhere though - I need R1 = as the 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

http://www.google.com/search?q=parallel+resistor+calculator

Then second hit is
http://www.electronics2000.co.uk/calc/series-parallel-resistor-calculator.php
Click to expand...
Thanks very much Robert - just what I needed!! (some basic reminding!! )
and also for the pointer...
Charlie+
 
Charlie+ wrote:
On Fri, 21 Aug 2009 12:48:50 +0200, Robert Roland <fake@ddress.no> wrote as:

On Fri, 21 Aug 2009 11:11:05 +0100, Charlie+ <charlie@xxx.net> wrote:

1/Rt = 1/R1 + 1/R2

Already done that - thats easy !
Doesnt get anywhere though - I need R1 = as the 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

http://www.google.com/search?q=parallel+resistor+calculator

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

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

(head shaking and finger wagging at your lack of self application)
 
On Fri, 21 Aug 2009 09:15:26 +0100, Charlie+ <charlie@xxx.net> wrote:

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
Click to expand...
R1 = - (1/((1/R2) + (1/R3) - (1/Rt)))
 
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:
Charlie+ wrote:
On Fri, 21 Aug 2009 12:48:50 +0200, Robert Roland <fake@ddress.no
wrote as:

On Fri, 21 Aug 2009 11:11:05 +0100, Charlie+ <charlie@xxx.net> wrote:

1/Rt = 1/R1 + 1/R2

Already done that - thats easy !
Doesnt get anywhere though - I need R1 = as the 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

http://www.google.com/search?q=parallel+resistor+calculator

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


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

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.

(head shaking and finger wagging at your lack of self application)
Click to expand...
 
On Fri, 21 Aug 2009 16:50:58 -0400, Hammy <spam@spam.com> wrote
R1 = - (1/((1/R2) + (1/R3) - (1/Rt)))
Thanks for your equasion - much easier than the one I home brewed in the
Click to expand...
end: R1=(RtR2R3)/(R2R3)-(RtR3)-(RtR2)
Both got to the correct answers in the application!
Charlie+
 
On Sat, 22 Aug 2009 02:11:07 +1000, David Eather <eather@tpg.com.au> wrote :


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.

(head shaking and finger wagging at your lack of self application)
Click to expand...
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+
 
Robert Roland wrote:
On Fri, 21 Aug 2009 11:11:05 +0100, Charlie+ <charlie@xxx.net> wrote:

1/Rt = 1/R1 + 1/R2

Already done that - thats easy !
Doesnt get anywhere though - I need R1 = as the 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
Click to expand...
-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.


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