Question

(1 point) In an LR circuit, L = 180 mH and R= 25 12. The switch is closed at t = 0. a) How long does it take to rise to 40% of its final value? ms b) What percentage of the final current is attained in 5 time constants? %

Answer 1

Answer-

(a) It will take 3.672 mS to rise to 40% of its final value.

(b) Final current is attained 99.32% of the final value in 5 time constants.

The circuit is a LR circuit, Lets take it! solution a series L-R circuit, where L = 180 mH & R = 252 switch is being closed at tao Lets draw the circuit 20 L mm + R V assume that supply voltage is = Instantaneous value of currentz bo and final value of current a I In the steady state inductor will get short circuited so final value of current will be I v R ☺ At to, when switch is closed, apply KVL in the circuit v=iRt L di olt

Take laplace transform Ži(s) R + L S ics) i (5o = V SCRALS) ri icso = VIL SCS+RL After partial fraction we get iles NIR VIR S STRIL jis 3 (A - Strin D Take inverso laplace transform -ßt in žlice . Equation 0 is equation of instantaneous current It also equation can be written as i. Ici-e Reg [: I să] I is the final value of current

(9) we have to find out the time at which current reaches 40% of its final value from equation ori 0.4 y = (1-éct) 0.4=1-ert -0.6=-PRO e Rt = 0.6 1 ooi Take logarithm both sides Ince- Rt I = Incool - Rt -0.510 0.510a L tz or, R Put the values of L2 180mH and R = 252 t = 0.510 x 180x1003 25 ta 3.672 810 3 seconds t 3.672 ms

so it will take 3.672 ms to rise to you. of its final value. 16) we know that the time constant of L-R circuit is: e = he so e 180x1003 25 2 7.2 710-3 sec e = 7.2 ms we have to find the percentage of the final eurrent is attained in 5 time constants ie. t = 50 From equation és (lae ci-e-Reg Ř ci-e the (1-e e ) R Here t = time constant we have to put t 250

so 50 iz ucl-ee iz ž (1-25) oy or i = (0.9932) GiD We know = I is final value of current from equation 1 it can be seen that at t25e current will reach gg. 32% of its final value. so at 5 time constants current will attain gg, 32% of its final value