# How to Calculate Equivalent Resistance with Kirchhoff's Laws?

• B4ssHunter
In summary, the conversation discusses a circuit with resistors connected in a way that creates a paradox. The voltage around R0 and R2 is supposed to be equal, but this would mean no current flows through the middle wire. However, the current does flow through the middle wire if there is a voltage difference, which would make R2 and R0 connected in parallel. The conversation also explores different scenarios and calculations related to resistors and current flow. Ultimately, the circuit is described as a balanced wheatstone bridge.
B4ssHunter
okay i have this somekind of a paradox
in the circuit below
voltage around R0 and R2 is supposed to be equal
now if it is equal , wouldn't that mean that the current will not pass through the middle vertical wire ?
and if it doesn't then this means that the resistors are now connected in parallel such that the above two are connected in series so are the two below , and thus i will not be able to say that they have the same voltage
while if we look at it from another point
such that the current does flow through the wire in the middle , thus the voltage around R2 and R0 is not equal * hence the current passed through the wire * then i can safely say that R2 and R0 are connected in parallel and therefore they have the same voltage across them ?
please please help me with it , even my teacher could not explain it to me .

please note that this is not a homework question , i have posted the homework part of this question in the homework forum , but in this case i have difficulty grasping the physical idea of connecting parallel resistors

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The connections between the resistors are equivalent to connecting the output of R0 and R2 together, then running a single line to the inputs of R1 and R3. Try drawing it that way and it will be clearer.

That little vertical wire will not carry current if there is no voltage difference, but it can and will carry current if a voltage difference were to start to form; this flow will be just enough to level out the voltage difference and ensure that the voltage at both of its ends will be the same.

It's like connecting two water tanks with a pipe so they'll both maintain the same water level.

Nugatory said:
The connections between the resistors are equivalent to connecting the output of R0 and R2 together, then running a single line to the inputs of R1 and R3. Try drawing it that way and it will be clearer.

That little vertical wire will not carry current if there is no voltage difference, but it can and will carry current if a voltage difference were to start to form; this flow will be just enough to level out the voltage difference and ensure that the voltage at both of its ends will be the same.

It's like connecting two water tanks with a pipe so they'll both maintain the same water level.

if there was a voltage difference
say R2 has more potential than R0 so electricity flows from R2 to R0 , i can consider the wire * if it has a resistance * to be connected in series with R0 so it consumes the extra potential leveling out the potential right ?

B4ssHunter said:
while if we look at it from another point
such that the current does flow through the wire in the middle , thus the voltage around R2 and R0 is not equal * hence the current passed through the wire * then i can safely say that R2 and R0 are connected in parallel and therefore they have the same voltage across them ?

According to Ohm's law current doesn't need a potential difference to flow in a zero resistance path.Hence current does flow in the middle wire.

quawa99 said:
According to Ohm's law current doesn't need a potential difference to flow in a zero resistance path.Hence current does flow in the middle wire.

oh then screw my physics teacher -_- ...
it would have been better if he just said * i don't know * -_-

B4ssHunter...

Whether the current would flow or not in the middle wire depends on the resistors R0,R1,R2,R3 .

If R2/R0 =R3/R1 then current doesn't flow ,else current flows .

Now whether current flows from top to bottom in the middle wire or bottom to top depends on the resistors.

Does this help ?

Tanya Sharma said:
B4ssHunter...

Whether the current would flow or not in the middle wire depends on the resistors R0,R1,R2,R3 .

If R2/R0 =R3/R1 then current doesn't flow ,else current flows .

Now whether current flows from top to bottom in the middle wire or bottom to top depends on the resistors.

Does this help ?

yes tanya this is very helpful , i have came to this conclusion 3 minutes earlier :p
any way , what if there is a resistor in the wore , and r2/r0 =/ r3/r1 .
how do i calculate the current going through the resistor in the wire ?

Well...then there is no current in the middle resistor .

B4ssHunter said:
if there was a voltage difference
say R2 has more potential than R0 so electricity flows from R2 to R0 , i can consider the wire * if it has a resistance * to be connected in series with R0 so it consumes the extra potential leveling out the potential right ?

If the wire has a resistance, then you have to draw it as a resistor - and of course there can be a voltage drop across a resistor.

If you haven't tried redrawing the diagram as I suggested above, do so. It will be a lot clearer (and if you don't see why that rearrangement is legitimate at first glance, figuring out why it is will steer you in the right direction).

Tanya Sharma said:
Well...then there is no current in the middle resistor .

in this case we treat the the upper resistors as if they were series * so do the lower two * and thus the whole thing is a parallel circuit right ? * just as if we removed the middle line *

Yes...you are right.

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B4ssHunter said:
in this case we treat the the upper resistors as if they were series * so do the lower two * and thus the whole thing is a parallel circuit right ? * just as if we removed the middle line *

That is exactly correct.It is a classical example of a balanced wheatstone bridge.

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Nugatory said:
If the wire has a resistance, then you have to draw it as a resistor - and of course there can be a voltage drop across a resistor.

If you haven't tried redrawing the diagram as I suggested above, do so. It will be a lot clearer (and if you don't see why that rearrangement is legitimate at first glance, figuring out why it is will steer you in the right direction).

i drew it the way you said
i think now since it has resistance , the first two resistors are not connected in parallel anymore Alone , the whole circuit is now parallel . not just the first two and the second two
and the middle wire is useless now
--
or i could be wrong and if i am
then if R2/R0 = R1/R3 then there will be no current going through the resistor
if R1>R3 , the current will flow more through R3 , thus it will flow R0 to R3 ,
so we consider R0 and Rmiddle to be in series and both of them connected in parallel to R2 .

B4ssHunter...If the middle line has a resistor and R2/R0 ≠ R1/R3 then some current flows through the middle resistor.In that case the resistors are neither in parallel nor in series .

But if R2/R0 = R1/R3 ,then the observation you made in post#10 is true .

Tanya Sharma said:
B4ssHunter...If the middle line has a resistor and R2/R0 ≠ R1/R3 then some current flows through the middle resistor.In that case the resistors are neither in parallel nor in series .

But if R2/R0 = R1/R3 ,then the observation you made in post#10 is true .

then what are they ?

It is not necessary for a group of resistors to be classified in either parallel or series .

A series circuit is a circuit in which resistors are arranged in a chain, so the current has only one path to take. The current is the same through each resistor.

A parallel circuit is a circuit in which the resistors are arranged with their heads connected together, and their tails connected together. The current in a parallel circuit breaks up, with some flowing along each parallel branch and re-combining when the branches meet again. The voltage across each resistor in parallel is the same.

Interesting observation in case R2/R0 = R3/R1

1) (R0 || R2 ) IN SERIES WITH (R1 || R3)

2) (R0 IN SERIES WITH R1) || (R2 IN SERIES WITH R3)

okay now i understand the situation when there is no resistor in the in the middle wire
now
if R0 = 2 ohms R2= 3 ohms R1 = 8 ohms and R3 = 4 ohms and the middle wire has a resistance of 1 ohm
can somebody calculate the total equivalent resistance ? just to know how i would calculate the middle resistor

B4ssHunter said:
okay now i understand the situation when there is no resistor in the in the middle wire
now
if R0 = 2 ohms R2= 3 ohms R1 = 8 ohms and R3 = 4 ohms and the middle wire has a resistance of 1 ohm
can somebody calculate the total equivalent resistance ? just to know how i would calculate the middle resistor
You can use kirchhoff's laws to calculate equivalent resistance.

## 1. How do you calculate the total resistance of parallel resistors?

When connecting parallel resistors, the total resistance is calculated using the formula: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + .... This means that the reciprocals of each individual resistance are added together and then inverted to find the total resistance.

## 2. What is the purpose of connecting parallel resistors?

Connecting parallel resistors allows for the total resistance of a circuit to be decreased. This is useful for controlling the amount of current flowing through a circuit and ensuring that individual components do not get overloaded.

## 3. How do you connect parallel resistors?

To connect parallel resistors, you simply connect each resistor's terminals to the same two points in the circuit. This forms a parallel branch, with each resistor connected directly to the power source and ground.

## 4. Can you mix different resistors in a parallel connection?

Yes, you can mix different resistors in a parallel connection. However, it is important to note that the total resistance will always be less than the smallest individual resistor. This is because the smaller resistor will allow more current to flow through it, reducing the overall resistance of the circuit.

## 5. What happens to the voltage across each resistor in a parallel connection?

The voltage across each resistor in a parallel connection will be the same. This is because each resistor is connected to the same two points in the circuit, and voltage is distributed evenly across all components in a parallel branch. However, the current flowing through each resistor may vary depending on the individual resistance values.

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