RL Circuit with Two Loops: Solving for Current and Switch Equation

In summary, the emf and two resistors are given values in a RL circuit. Kirchhoff's loop rule can be used to solve for the current through the switch and the inductor. However, the equation does not match the answer in the textbook, and it is unclear what the R in the second loop equation is.
  • #1
discoverer02
138
1
I have a homework problem with an RL circuit. There are two loops in the circuit. One has the emf and two resistors and a switch and the other has two resistors and an inductor. The resistors, the inductor and the emf are all given values and I'm given that the switch is closed at time = 0 and to find the equation for the current through the inductor and the switch for the time after t = 0.

I tried using Kirchhoff's loop rule to see what I could come up with but I after I related Itotal, I1, I2 and solved for
e^(-t/T) my answers didn't match the ones in the book.

Is my approach correct or am I missing something?

Thanks
 
Physics news on Phys.org
  • #2
IT will be helpful if you give fig and your try
 
  • #3
Kirchhoff's rules, yes, but the devil is in the details. If you're still stuck, let's see your equations.
 
  • #4
OK, I've posted a diagram.

I = I1 + I2

First Loop: 10V = 4ohmsI + 4ohmsI1
Second Loop: 10V = 4ohmsI + 8ohmsI2 + Ldi2/dt

If I divide both equations by 1 ohm:

First Loop: 10I = 4I + 4I1
Second Loop: 10I = 4I + 8I2 + L/R(di2/dt)

L/R = Time constant = T

4I1 = 6I
I1 = I - I2 so 4I2 = -2I ==> I = -2I2

Tdi2/dt + 8I2 = 6I
Tdi2/dt + 8I2 = 6(-2I2) = -12I2

Tdi2/dt = -20I2

di2/(20I2) = -1/T(dt)

integrate and ==> ln(20I2)/20 = e^(-t/T)

If I'm correct so far then this is where I get confused.

There's no emf in the second loop, so there's an initial current in the second loop?

I'm not sure which form of the equation for I in an RL circuit I should use. (no initial current, no emf, both) I'm also not sure that what I did with L/R above is valid.
 

Attachments

  • drawing1.bmp
    18 KB · Views: 743
Last edited:
  • #5
First loop should be:

10 = 4I + 4I1 (NOTE: 10, not 10I)

second loop:
10 = 4I + 8I2 + LdI2/dt

and L is 1 so you can leave it off & just say
10 = 4I + 8I2 + dI2/dt

I don't understand what that R is in your second loop equation, but the back emf is just LdI2/dt. No R.

Note also: you can also use as the second equation:
4I1 - 8i2 - dI2/dt
 
  • #6
Thanks gnome.

That was a silly error. I have no idea why I put that 'I' in the equation. For some reason I thought I was dividing through by R instead of 1 ohm. Too tired. I'm glad the semester's almost over.
 

1. What is an RL circuit?

An RL circuit is a type of electrical circuit that contains a resistor (R) and an inductor (L). The resistor limits the flow of current in the circuit, while the inductor stores energy in the form of a magnetic field.

2. What is the two loops problem in an RL circuit?

The two loops problem in an RL circuit refers to a circuit with two inductors connected in parallel, creating two separate loops for the current to flow through. This can complicate the analysis of the circuit and requires the use of special techniques such as Kirchhoff's laws and thevenin's theorem.

3. How do you calculate the total inductance in a two loop RL circuit?

To calculate the total inductance in a two loop RL circuit, you can use the formula L = L1 + L2 + 2M, where L1 and L2 are the individual inductances of the two loops and M is the mutual inductance between the two loops.

4. What is the significance of the mutual inductance in a two loop RL circuit?

Mutual inductance refers to the magnetic coupling between two inductors in a circuit. In a two loop RL circuit, the mutual inductance is significant because it affects the total inductance of the circuit and can also cause the two loops to interact with each other, creating complex behavior.

5. How do you solve a two loop RL circuit problem?

Solving a two loop RL circuit problem involves using Kirchhoff's laws, thevenin's theorem, and other techniques to analyze the circuit and calculate the current, voltage, and other parameters. It is important to properly label the loops, determine the total inductance, and apply the appropriate equations to solve for the unknown values.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
619
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
552
  • Introductory Physics Homework Help
Replies
18
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
67
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
22
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
207
  • Introductory Physics Homework Help
Replies
20
Views
255
  • Introductory Physics Homework Help
Replies
6
Views
1K
Back
Top