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Parallel resistors formula

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

Reply to
Charlie+
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parallel conductances are much easier.... do that.

write it like this:

1/Rt = 1/R1 + 1/R2
Reply to
Jasen Betts

On 21 Aug 2009 09:37:05 GMT, Jasen Betts wrote as

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!

Reply to
Charlie+

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

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Then second hit is

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RoRo
Reply to
Robert Roland

On Fri, 21 Aug 2009 12:48:50 +0200, Robert Roland wrote as:

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

Reply to
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)

Reply to
David Eather

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

Reply to
Hammy

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....

Mart> Charlie+ wrote:

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Reply to
Martin H. Eastburn

On Fri, 21 Aug 2009 16:50:58 -0400, Hammy wrote

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+

Reply to
Charlie+

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+

Reply to
Charlie+

-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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Reply to
Tom Del Rosso

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