Consider the current pulse i(t) shown in Figure a below. The current begins at z

Question

Consider the current pulse i(t) shown in Figure a below. The current begins at zero, becomes 10.0 A between t = 0 and t = 200 microseconds, and then is zero once again. This pulse is applied to the input of the partial circuit shown in Figure b below. (Let R = 104 ohm and L = 14.0 mH.) Determine the current in the inductor as a function of time. (Use the following variable as necessary: t. If the current in a range is always zero enter 0.)

for t between 0 and 200 microseconds i =

for t greater than 200 microseconds i =

Explanation / Answer

R = 104 ohm, L = 14.0 mH = 14 * 10-3 H

The current is rising in between t = 0 mus and 200 mus

I0 = 10.0 A

t = 200 * 10-6 s

-----------------------------------------------

for t between 0 and 200 microseconds

I = I0 [1 - e-t/T]

T = L / R

I = I0 [1 - e-Rt/L]

I = 10 * [1 - e-(104 * 200 * 10-6/14 * 10-3)]

I = 7.74 A

--------------------------------------------------

for t greater than 200 microseconds

I = I0 [1 - e-t'/T]

I = I0 [ e-R(t-200us)/L]

I = 7.74 [ e-104(t-200us)/14 * 10-3]

I = 7.74 [ e-7428.6t+1.4857]

I = (34.195 A )  e-7428.6t

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects