A circuit is constructed with four resistors, one inductor, one battery and a sw
ID: 1440566 • Letter: A
Question
A circuit is constructed with four resistors, one inductor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 40 , R3 = 64 and R4 = 130 . The inductance is L = 370 mH and the battery voltage is V = 12 V. The positive terminal of the battery is indicated with a + sign.
1) The switch has been open for a long time when at time t = 0, the switch is closed. What is I4(0), the magnitude of the current through the resistor R4 just after the switch is closed?
A
2) What is I4(), the magnitude of the current through the resistor R4 after the switch has been closed for a very long time?
A
3) What is IL(), the magnitude of the current through the inductor after the switch has been closed for a very long time?
A
4) After the switch has been closed for a very long time, it is then opened. What is I3(topen), the current through the resistor R3 at a time topen = 6.8 ms after the switch was opened? The positive direction for the current is indicated in the figure.
A
5) What is VL,max(closed), the magnitude of the maximum voltage across the inductor during the time when the switch is closed?
V
6) What is VL,max(open), the magnitude of the maximum voltage across the inductor during the time when the switch is open?
V
--wwT-L ETF R, R. R, 1 RP VExplanation / Answer
Here,
1) when the switch is just closed , the inductor will behave as an open circuit
I4(0) = V/(R1 + R3 + R4)
I4(0) = 12/(40 + 64 + 130)
I4(0) = 0.0513 A
2)
after a very long time
the inductor is short cicuited
Req = R1 + R2 * R3/(R2 + R3) + R4
Req = 40 + 40 * 64/(40 + 64) + 130
Req = 194.6 Ohm
I4(infinite) = 12/194.6
I4(infinite)=0.062 A
3)
after a very long time
Using current divider
IL(inifinite) = I4(inifinite) * R3/(R3 + R2)
IL(inifinite) = 0.062 * 64/(64 + 40)
IL(inifinite) = 0.0379 A
4)
time constant , T = 0.370/(64 + 40)
T = 3.56 *10^-3 s = 3.56 ms
let the current is I
IL = 0.0379 * (e^(-t/T))
IL = 0.0379 * e(-6.8/3.56)
IL = 5.605 *10^-3 A
the current is 5.605 *10^-3 A
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