Electric circuits formulas doubts

[thegreengineer]

Well, recently I have started to deal with electronics and I've seen several new concepts such as ohm's law, parallel and series circuits, what's AC and DC and many other topics.

Ok, I have no doubt on what's direct and alternate current or what a series and parallel circuits are; rather than that my main doubts focuses on how electric circuits formulas are used.

To clear this I'll put an example:
I connect three resistors in parallel, the first is a 3 Ω resistor, the second is a 6 Ω resistor, and the third is a 10 Ω resistor. They are connected in such circuit with a battery of 5 V. The current is worth 10 A.

If I had this as an example:

Question #1. Knowing that this is a parallel circuit and hence the total electric resistance is calculated through (in this case):
$\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$
Where does the total electric resistance fit? What does it represent?

Question #2. Supposing that I needed to calculate the voltage on each resistor
Does the voltage on each resistor need to be calculated with the ohm's law? I mean for example if I needed to calculate the voltage on the 6 Ω resistor I would use V=IR; however is the current to be used in the previous formula 10 A or must be calculated through $I_T=I_1+I_2+I_3$?

Sorry if this may sound annoying for some people, I'm learning and this has been always hard for me. Thanks.

 

[Drakkith]

Where does the total electric resistance fit? What does it represent?

Knowing the applied voltage and the resistance of each resistor allows us to find the current through each resistor, and from that the total current in the circuit. The formula for "total resistance" is merely a shortcut so that we don't have to calculate the current through each resistor individually if we only care about the total current through the circuit. Instead, we can find the total resistance and substitute that number into ohm's law to find the total current.

Question #2. Supposing that I needed to calculate the voltage on each resistor
Does the voltage on each resistor need to be calculated with the ohm's law? I mean for example if I needed to calculate the voltage on the 6 Ω resistor I would use V=IR; however is the current to be used in the previous formula 10 A or must be calculated through IT=I1+I2+I3I_T=I_1+I_2+I_3?

You would use the applied voltage and the resistance of each resistor to find the current through that resistor. The sum of the current through each resistor should add up to equal 10 amps.

 

[CWatters]

Where does the total electric resistance fit? What does it represent?

Instead of "total resistance" it might be better to use the word "equivalent resistance". I'll explain below..

connect three resistors in parallel, the first is a 3 Ω resistor, the second is a 6 Ω resistor, and the third is a 10 Ω resistor. They are connected in such circuit with a battery of 5 V. The current is worth 10 A[

I think you need to post your circuit diagram because there is something wrong. For the moment I will assume you have three resistors in parallel with a 5V battery and ignore that bit about "The current is worth 10 A".

First let's forget about total/equivalent resistance and work out the currents through each resistor..
V=IR so
I = V/R

The current through the 3 Ω resistor = 5/3 = 1.667
The current through the 6 Ω resistor = 5/6 = 0.833
The current through the 10 Ω resistor =5/10 = 0.5
Total current from battery = 1.667 + 0.833 + 0.5 = 3A (eg not 10A which is why I said there is something wrong).

Now let's work out the equivalent resistance...

1/Re = 1/(1/3 + 1/6 + 1/10)
gives
Re = 1.67 Ohms

So instead of three resistors in parallel we should be able to replace them with one resistor of 1.67 Ohms.

Now the total current from the battery will be 5/1.67 = 3A which is the same as before.

 

[CWatters]

Question #2. Supposing that I needed to calculate the voltage on each resistor

That will be the same 5V on all of them because they are all in parallel with the battery.

 

[thegreengineer]

CWatters thank you very much.

 

[Frapa]

Sometimes it is useful to make the analogy with water circuits. In this analogy resistors are like pipes, the higher the resistance the thinner the pipe (so that it offers more resistance to the flow of water). Voltage is like pressure and a battery is a pump.

Putting 3 pipes in parallel makes the resistance less (with the formula you quoted) because it gives current more paths to flow in.

Don't press the analogy too far, but think of it if you find an example difficult.