Something I don't understand in Circuit

[Genericcoder]

Hi guys,

Their is something I don't completely understand regards to parrallel/series circuits.

We know that the resistance can be calculated as follows in series:-

Since they total voltage is the sum of the voltage components:-

V = V1 + V2 + V3;
IR = IR1 + IR2 + IR3;
R = R1 + R2 + R3;

In Parrallel circuits it can be calculated as follows:-

I = I1 + I2 + I3;
V/R = V/R1 + V/R2 + V/R3;
1/R = 1/R1 + 1/R2 + 1/R3;

What I don't understand is can we also use second formula(the one of parrallel circuits) to calculate in series,because we know that current don't accumulate(conserved),so the I starting before going into any resistor that I should be the one as one that comes out of last resistor.

So the in series then would be same equation as parallel circuit would that makes sense or did I miss something here?

Thanks.

 

[cepheid]

No, for a series circuit, it would be

I = I1 = I2 = I3

because the current must be the same everywhere in the loop.

If the current was larger at some point in the loop than at another point, then you'd get a pile up of charge that would in turn lead to an emf that would in turn tend to smooth out the charge distribution.

 

[Genericcoder]

Sorry for late reply had no internet,but if I1 = I2 = I3 wouldn't that have same form as parrallel circuits which would be

I = 1/R1 + 1/R2 + 1/R3 etc coz all current that is going out of certain junction is same as current going?

 

[cepheid]

Sorry for late reply had no internet,but if I1 = I2 = I3 wouldn't that have same form as parrallel circuits which would be

I = 1/R1 + 1/R2 + 1/R3 etc coz all current that is going out of certain junction is same as current going?

Hi Genericcoder,

The two situations are actually quite different. In the parallel case, each resistor is connected directly across the voltage source. As a result, the voltage across each resistor is the same, and is equal to the source voltage. In contrast, the current in each resistor is different, and depends on the particular resistance value, in accordance with Ohm's law. However, the sum of the currents through all the resistors must be equal to the total current provided by the source. As a result, for the parallel case, we have:

parallel case:

V = V1 = V2 = V3

I = I1 + I2 + I3

In the series case, we have the exact opposite situation for voltages and currents. The voltages across the resistors are all different, but they must add up to the voltage of the source, since the series combination of them is connected across the source. The current in all three resistors is the same, since they are all part of a closed loop. Therefore:

series case:

V = V1 + V2 + V3

I = I1 = I2 = I3

You see by looking at the equations for the two cases, how they different, right?

Let's compute the effective resistance "R" for the parallel case. It must be true that I = V/R. However, due to Ohm's law, this relation must be true for each resistor as well:

I1 = V1/R1

I2 = V2/R2

I3 = V3/R3

And since I1 + I2 + I3 = I, it follows that:

V/R = V1/R1 + V2/R2 + V3/R3

Remembering that all voltages are the same, we end up with:

V/R = V/R1 + V/R1 + V/R3

Divide both sides by V:

1/R = 1/R1 + 1/R2 + 1/R3

For the series case, it also must be true that I = V/R. However, it happens to be more useful to express this as V = IR in this case. Ohm's law also holds true for every individual resistor so that:

V1 = I1R1
V2 = I2R2
V3 = I3R3

Now, since the voltages have to add up to the total voltage, it must be true that

IR = I1R1 + I2R1 + I3R3

Now, since the current is the same everywhere, this becomes:

IR = IR1 + IR2 + IR3

R = R1 + R2 + R3.

So you see how the difference above led to different results. In the parallel case, all the voltages were the same, and it was the currents that had to add up to the total current. In the series case, all the currents were the same, and it was the voltages that had to add up to the total voltage.

Make sense?

 

[Genericcoder]

Yes that makes perfect sense.
Thanks alot.