RL circuit time constant question

[supra_tt]

Hi,

Was hoping someone could help me.

I have the following RL circuit:

20V input
8.2kohm resistor and 50mH Inductor in series.


Determine time constant:

I answered with: T = L/R 50mH / 8.2kohm

= 6.09 uS

Is this correct?

The question I am stuck on is:

Determine the value of VL after 1.5 time constants?

I have the formula, VL = E ( e - t / T)

I can't work out what to put for the t? I tried putting in:

20 (e - 1.5 / (6.09uS) but can't be right?

If someone could help I would be much appreciated

Thanks!

 

[ehild]

1.5 time constant means that that t/T=1.5. Substitute 1.5 for t/T into the formula of VL, but do not forget using parentheses.

ehild

 

[supra_tt]

Thanks for the quick response!

I am getting VL = 4.46V, I was wondering if you could please confirm this?

I am a little confused because the teacher has written the answer as VL = 15.54V

Does this mean I just need to take 4.46 from 20 to get the answer?

Thanks again

 

[ehild]

VL(t) is different if the source is switched on or off at t=0. You calculated VL after the battery is switched off. In case of switching on, VL=E(1-e^-t/T).

ehild

 

[Nickie]

Hi there,

Your calculation for the time constant is correct. To determine the value of VL after 1.5 time constants, you can use the formula VL = E (1 - e^-t/T), where t is the time in seconds. In this case, t would be 1.5 times the time constant, which is 1.5 * 6.09uS = 9.135uS. Therefore, the value of VL after 1.5 time constants would be VL = 20(1 - e^-9.135uS/6.09uS) = 9.62V.

Hope this helps! If you have any further questions, feel free to ask.