Solve RL Circuit Problem: V, I, P, w, w(0)

In summary, the conversation discusses finding the value of the resistor Rx and the initial current in a circuit using equations involving voltage, current, power, and energy. The individual uses a calculator to find estimates for the values and also integrates the power equation to determine the energy. However, it is suggested to find the time constant from a data point on the provided graph to obtain more accurate results.
  • #1
Mr. Johnson
22
0

Homework Statement


[PLAIN]http://img14.imageshack.us/img14/4355/screenshot20110807at249.png [Broken]


Homework Equations




v(t) = Vmax * e^(-Rt/L)
i(t) = imax * e^(-Rt/L)
P = V^2/R
w = integral of power w/ respect to time
w(0) = .5Li^2(0) = energy stored in inductor


The Attempt at a Solution



Well for #3, for the estimates of I and R, all I did was put the v(t) = Vmax*e^(-Rt/L) in my calculator w/ Vmax as 60 and L as 40mH. I played around with different R values and found that if I put R =1, the graph in my calculator is identical to the one as above.

To solve for I (current source), I used V = IR => I = 60 Amps.

For #4, I just used the energy equation w(0) = .5Li^2(0)
= .5*40e^-3 * 60^2 = 72 Joules

For #5, I integrated the power w/ respect to time to get the energy. But first I needed to solve for the power equation. P = V^2(t)/R where v(t) = -60e^(-t/40e^-3) and R = 1.

So then the energy equation was then the integral of 3600e^(-50t) dt from 0 to .02 milli seconds, which equals .716412 Joules.

The percentage = .07164/72 * 100 = .1%

I don't feel good about these answers and not sure if I did them right. Any help would be greatly appreciated.

Thank you.
 
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  • #2
You should be able to find a reasonably good value for the time constant (rather than mucking about with trial and error curve fitting) by taking a data point from the provided graph. I see that the voltage decays through the 5V level at t = 0.1ms...

With the time constant in hand, a reasonably accurate value for the resistor Rx can be found, and then the initial current... etc.
 

1. What is an RL circuit?

An RL circuit is a type of electrical circuit that contains a resistor (R) and an inductor (L) connected in series. These two components interact to create a time-varying current flow through the circuit.

2. How do I solve an RL circuit problem?

To solve an RL circuit problem, you will need to use the principles of Ohm's law and Kirchhoff's laws. This involves finding the total resistance (R) and inductance (L) in the circuit, calculating the current (I) using Ohm's law, and then using Kirchhoff's laws to determine the voltage (V) and power (P) in the circuit.

3. What is the relationship between current (I) and voltage (V) in an RL circuit?

In an RL circuit, the voltage and current are not in phase with each other due to the presence of the inductor. The voltage leads the current by 90 degrees, and the amplitude of the current is inversely proportional to the inductance.

4. What is the resonant frequency (w) in an RL circuit?

The resonant frequency (w) in an RL circuit is the frequency at which the inductive reactance (XL) is equal to the resistance (R). This results in a maximum current flow through the circuit and a minimum impedance, allowing for efficient power transfer.

5. What is w(0) in an RL circuit?

In an RL circuit, w(0) represents the resonance frequency when there is no resistance present in the circuit. This is known as the natural or undamped frequency and is determined by the inductance (L) and capacitance (C) in the circuit.

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