Calculating Equivalent Resistance of Resistor Network

In summary, the goal is to find the equivalent resistance of the infinite circuit shown in the image. By using recursion, it can be determined that the equivalent resistance is equal to R multiplied by Rl divided by R plus Rl, plus Rt. This can be simplified to R multiplied by Rl plus Rt, divided by R plus Rl.
  • #1
jesuslovesu
198
0

Homework Statement



Show that the equivalent resistance is Req = 1/2 [(4RtRl + Rt^2)^(.5) + Rt]
http://img74.imageshack.us/img74/5905/pingib2.png [Broken]

Homework Equations


The Attempt at a Solution



So far all I can get is Req = Rt + Rl Rt/(Rt+Rl) from the first three resistors starting from the left. I suppose I could take that and add it to the next branch Rl Rt/(Rt+Rl), but that would appear to go on to infinity as opposed to stopping at a nice number.

Does anyone have any hints on finding the eq. resistance?
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
I believe by recursion.

Everything to the right of RL is parallel with RL, and in series with RT.
 
  • #3
Since this is an infinite circuit, ignore the first rt and rl, and assume the resistance of the rest to be R. This give you:

R*rl/(R+rl) +rt=R. As the resistance of the total circuit is also R. Solve for R to get your answer.
 

What is equivalent resistance?

Equivalent resistance is the combined resistance of a group of resistors in a circuit that can be replaced by a single resistor without changing the overall current or voltage in the circuit.

Why is calculating equivalent resistance important?

Calculating equivalent resistance is important because it allows us to simplify complex circuits and make them easier to analyze. It also helps us determine the overall resistance of a circuit, which is necessary for calculating current and voltage.

How do you calculate equivalent resistance for a series circuit?

In a series circuit, the equivalent resistance is simply the sum of all the individual resistances. This can be calculated by adding the values of each resistor in the circuit.

How do you calculate equivalent resistance for a parallel circuit?

In a parallel circuit, the equivalent resistance is calculated using the formula: 1/Req = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn. This means that the equivalent resistance is always less than the smallest individual resistance in the circuit.

What factors can affect the accuracy of calculating equivalent resistance?

The accuracy of calculating equivalent resistance can be affected by various factors, such as the accuracy of the individual resistance values, the temperature of the resistors, and the presence of any external factors, like stray capacitance or inductance. It is important to use precise measurement equipment and consider any external factors when calculating equivalent resistance.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
627
  • Introductory Physics Homework Help
Replies
24
Views
1K
  • Introductory Physics Homework Help
2
Replies
60
Views
7K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
6K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
2K
Back
Top