How do i calculate missing resistance readings in a parallel circuit using R1 and Rt

[Lucien Nunes]

But a numerical question would not normally require you to guess, therefore Mike's observation that the dash was intended to mean that there was no R3 present in that example, seems more likely.

 

[Lister1987]

The missing value should be lower than your lowest value resistor irrc.

Is this a series (R1) and parallel (R2 & R3) circuit, sounds like it, in which case you'll be wanting product over sum to help with missing value.

When ive had sleep, I'll dig out my notes and revisit this.
See here; Series and Parallel Resistors - https://learnabout-electronics.org/Resistors/resistors_20.php

 

[marconi]

MikeGawan: You might want to learn a new wrinkle to deal with series and parallel problems of resistors which only requires addition(+) and subtraction(-).

In series circuits the total resistance is easily calculated by adding together the individual resistance values viz: 3 + 2 +10 = 15Ohms.

In parallel circuits one can also add together the individual conductances; the conductance(C) of a resistor(R) is the reciprocal of its resistance ie C = 1/R - a resistor with a high resistance has then a low conductance and vice versa.

So, by way of example, if the 3, 2 and 10 resistors were all in parallel one adds together the reciprocals of these values to find the total conductance ie: 1/3 + 1/2 + 1/10 = whatever it comes to.

In the problem you are set, if you work with conductances from the start you just have to remember to take the reciprocal at the end to turn the unknown conductance into a resistance.

Example: 1, 2 and R are all in parallel and the total resistance is 0.1 Ohms or total conductance 10Mhos/Siemens - what is R?

1/1 + 1/2 + 1/R = 1/0.1

=> 1 + 0.5 + C = 10

==> C = 10 - 1- 0.5 = 8.5Mhos or Siemens

R =1/C = 1/8.5 =.... whatever Ohms

The algebra is no different to be honest but if one thinks in terms of conductance for items in parallel and resistance for items in series then it may play out more easily in your mind when tackling these problems. Always put the units in so you know whether a number is resistance value or a conductance value.

It helps too if you have a 'mental model' of the way electrons move through a conductor and what restricts their easy flow - what we call resistance. So, there are more restrictions to easy flow when resistors are in series because all the electrons leaving the first resistor then have to pass through the next and then the next...

When the resistors are in parallel not all the electrons go through all the resistors - the electrons have as many options as there are parallel paths to take - so overall there is less impediment because their flow from the input to the output side of the parallel resistor network is via as many routes as there are parallel resistors but those routes with lower resistance (higher conductance) take a proportionately higher number of electrons. Or something like this - you get the gist...