Solve LR Circuit Problem: Find New Values for R & Vo

AI Thread Summary
To achieve a time constant T that is half as long in an LR circuit, the resistance R must be reduced. The original resistance is 2200 ohms, and to maintain the same steady-state current while adjusting R, the voltage Vo must also be recalibrated. The relationship T = L/R indicates that decreasing R will increase the time constant, thus requiring a careful balance with Vo. The discussion emphasizes the need to simplify the problem by focusing on the steady-state current rather than the transient behavior. Ultimately, the solution involves determining new values for R and Vo that satisfy these conditions.
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Homework Statement

If You want to turn on the current through a coil of self inductance L in a controlled manner, so you place it in series with a resistor R= 2200 ohm, a switch, and a dc voltage source Vo=240 V. After closing the switch, you find that the current through the coil builds up to its steady=state value with a time constant T. You are pleased with the current's steady-state, but want T to be half as long. What new values should you use for Rand Vo.?

Homework Equations


T=L/R
I= Vo/R (1-e^(-t/T))

The Attempt at a Solution


I= 240/2200(1-e^(-t/T))
I'= Vo'/R'(1-e^(-2t/T))

Since, I=I'
240/2200(1-e^(-t/T))=Vo'/R'(1-e^(-2t/T)

Can somebody point out what I am missing here? Thanks
 
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You have the formula for the time constant T = L/R. You need the time constant to become half... so what do you need the R to become?

The steady state value of the current is Vo/R. considering the change in R above, what do you need to do to Vo to keep the same steady state current as before? We don't want I = I'... we only want the steady state I to be equal to the steady state I'.
 
Thanks...Got it...I was making it more complex than it was.
 
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