Question 1

Why in a circuit with several branches the voltage drop across each of the branches is the same? 
Why doesn't it also split up as the current?

Accepted Answer

Hi,

Here's an analogy that might help you understand:

Imagine there is a bakery, and it produces 5 slices of bread/min and there's 60g of carbo per slice of bread. 
If you own the production for yourself, you get 5 bread/min, and 60g carbo/bread.
If you are sharing with 4 other friends and you are dividing the bread evenly, you are getting only 1 bread/min, but still 60g carbo/bread.

In this analogy, 
the bakery=battery
You and your friends=//resistors
Bread production=flow of electrons
Bread=electrons' charge, measured in C.
Carbo=energy, measured in J.
Time is, well, time. 
Therefore carbo/bread=J/C, which is the voltage; 
bread/min=C/s, which is the current.

Here we can see that the voltage doesn't drop with //resistors, but the current does.

(This is not a proof, but only a way to understand)

Question 2

It is given that the resistor with the biggest resistance has the greatest voltage. We know that electric current is directly proportional to the potential difference across a circuit. So, this statement now means that the biggest resistance allows the largest amount of current to flow through it. Isn't this fact contradictory to what we have learnt? (Current is inversely proportional to resistance)

Accepted Answer

V=IR can be rearranged to I=V/R therefore while the resistance increases the current decreases.  In series, the current is the same throughout the circuit.  So, a  larger resistor will have a larger voltage drop.

If I have a larger resistor in parallel with a smaller resistor and they both have the same voltage applied since they are in parallel, which one do you think has more current flowing through?

Question 3

what if there are 2 resistors in series that are parallel to 1 other resistor?

Accepted Answer

In these types of cases it is best to simplify parts of the circuit and then find out the net resultant. In your example let each of the resistors individually have a value of resistance R. Then: 
The equivalent resistance of the resistors in series
Req1= R + R = 2R
Now as you mentioned, these two in series, are in parallel to one other resistor R.
Finding Req1 basically gives us that a single resistor of 2R would perform the same function(in this case) as the 2 resistors R in series.

So we can instead, now consider, a resistor with resistance Req1 to be in parallel combination to a resistor with resistance R. And we know how to do this:
1/ReqFinal= 1/Req1 + 1/R
Now, as Req1=2R, we get:
1/ReqFinal= 1/2R + 1/R = 3/2R
i.e: ReqFinal=2R/3
Which is the equivalent resistance of the whole combination!
You can extend this to more complex circuits as well, simplify parts of it and keep going!
Cheers!

Question 4

I need help in understanding Series-Parallel circuits, where there are both circuits in series and parallel in one individual circuit.

Accepted Answer

It would help to just solve the resistance for the parallels first and then add it to the total resisters.

for example if you had a 5 ohm resistor in series with parrallel resistors (8 and 8 ohms)
then you could do the parrallel resistors first and once you get the resistors value (4 ohms)
you could add it to the 5 ohm resistor (9 ohms)

Think of parrallel resistors as if they are combined to make one resistor

Equation	Symbol breakdown	Meaning in words
$\begin{aligned} R_{s} & = \sum_{i} R_{i} \\ or \\ R_{s} & = R_{1} + R_{2} + … \end{aligned}$ ‍	$R_{s}$ ‍ is equivalent series resistance and $\sum_{i} R_{i}$ ‍ is the sum of all individual resistances $R_{i}$ ‍.	Equivalent series resistance is the sum of all the individual resistances.
$\begin{aligned} \frac{1}{R_{p}} & = \sum_{i} \frac{1}{R_{i}} \\ or \\ \frac{1}{R_{p}} & = \frac{1}{R_{1}} + \frac{1}{R_{2}} + … \end{aligned}$ ‍	$R_{p}$ ‍ is equivalent parallel resistance and $\sum_{i} \frac{1}{R_{i}}$ ‍ is the sum of all individual resistances $R_{i}$ ‍ reciprocals.	The reciprocal of the equivalent parallel resistance is the sum of all the individual resistance reciprocals.

Course: AP®︎/College Physics 1 > Unit 11

Resistors in series and parallel review

Key terms

Equations

Resistors in series and parallel

Series resistor properties

Parallel resistor properties

How to calculate equivalent resistance

Equivalent series resistance

Equivalent parallel resistance

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