Find equivalent resistance in this circuit?

In summary, the homework statement is trying to find the equilivant resistance in a wheatstone bridge circuit. The attempt at a solution found that R3 is in series with R1 and R2. The equilivant resistance is found to be between 170 and 180 ohms.
  • #1
tlrmaus
8
0

Homework Statement


Find the equilivant resistance in the wheatstone bridge circuit.
Here is a picture: http://sub.allaboutcircuits.com/images/00485.png

Homework Equations



The Attempt at a Solution


I know R1 and R2 are in parallel and R4 and R5 are in parralel but I'm getting confused with R3.
When I find R12 and R45, would R3 be in series?
 
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  • #2
Things are in parallel when their ends are connected together. R1 and R2 both ends are not touching each other as R3 is between them.

Generally, there is formula for converting this kind of circuit into simpler form.

http://en.wikipedia.org/wiki/Y-Δ_transform
 
  • #3
An easy way to do this is to use Thevenin's equivalent.

If you remove the 100 ohms resistor, you can work out the voltages across where it was.
The difference between these is called the Thevenin voltage.

Now, connect the 150 ohm and 300 ohm R's in parallel and connect this in series with the 50 ohm and 250 ohm R's in parallel. Easy with a calculator.

This is called the Thevenin resistance.

Now, put the Thevenin voltage in series with the Thevenin resistance and the 100 ohm resistance. Work out the total current. This is the current in the 100 ohm resistance.
Call it I100

(This is easier with real numbers.)

Now, you need the voltage across the 250 ohm resistor.

V250= I250* 250 ohms
V250=24 - ((I100+I250 )* 50 ohms)

Solve this for the values of I250 and V250

After this, it is easy to work out all the currents and voltages and hence to find the equivalent resistance of the circuit.
Req= 24 V / I total
 
  • #4
Trying a method, different from those suggested, that I think I remember from about 50 years ago, I got an equivalent resistance between 170 and 180 ohms (not to give the answer away in case I actually have it right). From someone who knows how to do this problem, am I close?
 
  • #5
LCKurtz said:
Trying a method, different from those suggested, that I think I remember from about 50 years ago, I got an equivalent resistance between 170 and 180 ohms (not to give the answer away in case I actually have it right). From someone who knows how to do this problem, am I close?

Yes.

Did you use Kirchhoff Law equations?
 
  • #6
vk6kro said:
Yes.

Did you use Kirchhoff Law equations?

Yes. I summed the voltage drops around each loop to zero, solved for the current in the battery loop and calculated R = E/I.
 
  • #7
I found the current going through all the resistors so can I just use Req = V / I?
V being 24 and I being I1 + I2 + I3 + I4 + I5.
 
  • #8
No,

The current you need is the current leaving or returning to the battery.
 
  • #9
ok i figured it out. is the answer suppose to be 175 ohms?
 
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  • #10
The total current in R1 and R2 should equal the total current in R4 and R5.

It is this current you need.

Could you list your results?
 
  • #11
Yeah the current in R1 and R2 does = the current in R4 and R5. I'm just wondering why would that work?

Thanks vk6r0.
 
  • #12
The current leaving the battery has to equal the current returning to the battery.

What was your result?
 

FAQ: Find equivalent resistance in this circuit?

1. How do I determine the equivalent resistance in a circuit?

To determine the equivalent resistance in a circuit, you can use the formula R = V/I, where R is resistance, V is voltage, and I is current. You will need to know the values of voltage and current in the circuit.

2. What is the purpose of finding the equivalent resistance in a circuit?

The purpose of finding the equivalent resistance in a circuit is to simplify the circuit and make it easier to analyze. It allows you to replace multiple resistors with one equivalent resistor, making calculations and predictions more straightforward.

3. Can the equivalent resistance in a circuit be greater than the sum of individual resistances?

Yes, the equivalent resistance in a circuit can be greater than the sum of individual resistances. This is because resistors in parallel will have a lower equivalent resistance than resistors in series. Therefore, the equivalent resistance can be greater than the sum of individual resistances.

4. How does the arrangement of resistors affect the equivalent resistance in a circuit?

The arrangement of resistors affects the equivalent resistance in a circuit. Resistors in parallel will have a lower equivalent resistance, while resistors in series will have a higher equivalent resistance. The arrangement can also affect the overall current and voltage in the circuit.

5. Can I use the equivalent resistance to calculate the power dissipated in a circuit?

Yes, you can use the equivalent resistance to calculate the power dissipated in a circuit. You can use the formula P = V^2/R, where P is power, V is voltage, and R is resistance. The equivalent resistance will give you a more accurate calculation than using individual resistances.

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