I\'m confused with how to set up this question. My mainquestion is there a formu

Question

I'm confused with how to set up this question. My mainquestion is there a formula that relates V and R to L when you arenot given current? Below is the question as it is stated inthe book. You want to turn on the current through a coil ofself-inductance L in a controlled manner so you place it in serieswith a resistor R = 2200 , a switch, and a dc voltage sourceV0 = 240 V. After closing the switch, you findthat the current through the coil builds up to a steady-state valuewith a time constant . You are pleased with thecurrent's steady-state value, but want to be half aslong. What new values should you use for R andV0? Any help on this will be greatly apperciated. I'm confused with how to set up this question. My mainquestion is there a formula that relates V and R to L when you arenot given current? Below is the question as it is stated inthe book. You want to turn on the current through a coil ofself-inductance L in a controlled manner so you place it in serieswith a resistor R = 2200 , a switch, and a dc voltage sourceV0 = 240 V. After closing the switch, you findthat the current through the coil builds up to a steady-state valuewith a time constant . You are pleased with thecurrent's steady-state value, but want to be half aslong. What new values should you use for R andV0? Any help on this will be greatly apperciated.

Explanation / Answer

   Steady state current in RLcircuit   I0   =   V0/ R                                                                 =   240/ 2200                                                             =   6/55   A    Timeconstant      1   =   L/ R    For     timecostant to have half thevalue,   2   =   (1/2)* 1                                                                          L/ R'   =      L /2 *R                  

      comparing        newresistance   R'   =   2* R                                                             =   2* 2200                                                             =   4400            Newvoltage,   V'   =   I0* R'                                  =   (6/55)* 4400                                  =   480   V    Newvoltage,   V'   =   I0* R'                                  =   (6/55)* 4400                                  =   480   V

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