Electric circuits formulas doubts

• thegreengineer
In summary: Question In summary, CWatters is unsure of how formulas are used to calculate current in electric circuits.
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.

MarcusAu314 said:
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.

MarcusAu314 said:
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.

MarcusAu314 said:
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.

thegreengineer
MarcusAu314 said:
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.

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.

1. What is the most basic formula for electric circuits?

The most basic formula for electric circuits is Ohm's Law, which states that the current (I) flowing through a conductor is directly proportional to the voltage (V) and inversely proportional to the resistance (R). It can be represented as I = V/R.

2. How do you calculate the total resistance in a series circuit?

In a series circuit, the total resistance (Rtotal) can be calculated by adding up the individual resistances. So, Rtotal = R1 + R2 + R3 + ...

3. What is the difference between a parallel circuit and a series circuit?

In a series circuit, all components are connected in a single loop, so the same current flows through each component. In a parallel circuit, the components are connected in multiple branches, so the total current is divided among them.

4. How do you calculate power in an electric circuit?

Power (P) in an electric circuit can be calculated using the formula P = VI, where V is the voltage and I is the current. Alternatively, it can also be calculated using the formula P = I2R, where R is the resistance.

5. What is the difference between AC and DC circuits?

AC (alternating current) and DC (direct current) circuits differ in the direction of the current flow. In AC circuits, the current periodically changes direction, while in DC circuits, the current always flows in the same direction. AC circuits are commonly used for household electricity, while DC circuits are used in batteries and electronic devices.

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