Solve RL Circuits Problem: Find i(t) for t>0

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In summary, the problem is to find i(t) for t>0 for the given circuit. To simplify the resistors, a Wye-Delta transform is used. After that, the Kirchoff current law is applied to the nodes to calculate i(o). The main difficulty is in determining i(o). Various methods, such as solving a differential equation, can be used to find the transient current through the inductor.
  • #1
pukeynut
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Homework Statement


For the circuit shown, find i(t) for t>0
http://img440.imageshack.us/img440/5158/cicuit.jpg



Homework Equations


To simplify the resistors we use a Wye-Delta transform so:
R1 = RbRc/(Ra+Rb+Rc)
R2 = RcRa/(Ra+Rb+Rc)
R3 = RaRb/(Ra+Rb+Rc)

Then the Kirchoff current law on the nodes to calculate i(o).


The Attempt at a Solution



I can do the Wye-Delta transform no problem, but am having serious trouble in calculating i(o). After that it's a fairly straightforward problem.

Any help would be massively appreciated!
 
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  • #2
What have you tried? What's giving you trouble?
 
  • #3
pukeynut said:
For the circuit shown, find i(t) for t>0.
Will you be determining a differential equation, then solving it, to find the transient current through the inductor? Or what method will you be using?
 

Related to Solve RL Circuits Problem: Find i(t) for t>0

1. How do I approach solving an RL circuit problem?

To solve an RL circuit problem, you will need to use Kirchhoff's voltage law and Faraday's law of induction. First, draw a circuit diagram and label all known values. Then, use Kirchhoff's voltage law to write an equation for the total voltage in the circuit. Next, use Faraday's law to write an equation for the voltage across the inductor. Finally, solve the two equations simultaneously to find the current as a function of time.

2. What is the difference between a series RL circuit and a parallel RL circuit?

In a series RL circuit, the resistor and inductor are connected in a single loop, whereas in a parallel RL circuit, they are connected in separate branches. This affects the way the current and voltage are distributed in the circuit. In a series RL circuit, the current is the same in both components, while in a parallel RL circuit, the voltage is the same across both components.

3. How do I calculate the time constant in an RL circuit?

The time constant in an RL circuit is equal to the ratio of the inductance (L) to the resistance (R). It is represented by the symbol τ = L/R. This value determines how quickly the current in the circuit will reach its maximum value.

4. What is the significance of the initial conditions in solving an RL circuit problem?

The initial conditions, such as the initial current (i0) and initial voltage (v0), play an important role in solving an RL circuit problem. These values are used to determine the constants of integration in the solution, which in turn affect the behavior of the current in the circuit. Without considering the initial conditions, the solution may not accurately reflect the actual behavior of the circuit.

5. How can I check my solution for an RL circuit problem?

You can check your solution for an RL circuit problem by verifying that it satisfies Kirchhoff's voltage law and Faraday's law of induction. Additionally, you can use a circuit simulator program or an oscilloscope to compare the predicted and actual values of current over time. It is also helpful to double-check your calculations and make sure they are consistent with the given circuit parameters.

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