Solving a Simple RL Circuit: Find My Fault!

In summary, the conversation discusses a first order circuit problem and the use of Laplace transforms to solve it. The problem involves determining the time constant and initial and final conditions for the current through an inductor. The conversation also considers the effect of opening a switch and the paths available for current to flow.
  • #1
rbwang1225
118
0

Homework Statement


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circuit.jpg


The Attempt at a Solution


[itex]V-R_1I_1-LdI_L/dt=0, V-R_1I_1-R_2I_2=0, I_1=I_L+I_2[/itex]
My result is [itex]I_L=(V/R_1)(1-exp[-tR_1R_2/(R_1+R_2)L])[/itex]
Where is my fault?
Any help is appreciated!
 
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  • #2
have you learned laplace transforms? it is probably unnecessary in this case but the safest way to do problems like this.
 
  • #3
This being a first order circuit (only one type of reactive component), you know that the resulting waveforms for all the transient values (currents, voltages) will involve decaying exponential functions with a particular time constant. If you can determine the initial conditions and the final conditions, then the exponential functions will connect the two. Simple! The only really tricky bit is determining the time constant, [itex] \tau [/itex].

The problem statement says that the switch is initially closed (prior to time t = 0). So what is the steady-state current through the inductor, and hence the initial current for time t=0+? When the switch is opened, what paths are available for current to flow? So what components determine the time constant? What's the eventual value of the inductor current?
 

Related to Solving a Simple RL Circuit: Find My Fault!

1. What is a simple RL circuit?

A simple RL circuit is a circuit that contains only a resistor (R) and an inductor (L) connected in series. It is a basic circuit used to study the behavior of inductors and their effects on current flow.

2. How do I solve a simple RL circuit?

To solve a simple RL circuit, you will need to use Kirchhoff's laws and Ohm's law. First, use Kirchhoff's voltage law to determine the total voltage in the circuit. Then, use Ohm's law to calculate the current in the circuit. Finally, use Kirchhoff's current law to find the voltage drop across each component in the circuit.

3. What is the purpose of finding faults in a simple RL circuit?

The purpose of finding faults in a simple RL circuit is to identify any issues or malfunctions in the circuit that may be causing a decrease in performance or a complete failure. By finding and fixing these faults, the circuit can operate efficiently and effectively.

4. How do I find faults in a simple RL circuit?

To find faults in a simple RL circuit, you can perform a variety of tests such as measuring the voltage and current in different parts of the circuit, checking for loose connections or damaged components, and using a multimeter to test for continuity and resistance. It may also be helpful to create a circuit diagram and compare it to the actual circuit to identify any discrepancies.

5. What are some common faults in a simple RL circuit?

Some common faults in a simple RL circuit include open circuits (broken connections or damaged components), short circuits (when two points in the circuit are unintentionally connected), and excessive voltage drops (due to high resistance or damaged components). Other issues may include incorrect wiring, wrong component values, or incorrect circuit design.

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