1. What is a time constant? 2. What is a transient? 3. What is the time constant

Question

1.     What is a time constant?  

2.     What is a transient?

3.     What is the time constant ? for the circuit in Figure 7.1?

4.     What is the transient time for the circuit in Figure 7.1?

5.     What is the value of the current IL   through the inductor at the beginning and the end of the charge cycle?

6.     What is the voltage VL   across the inductor and the resistor at the beginning and the end of the charge cycle?

7.     How does the inductor act at the beginning and end of the charging process (short or open)?

8.     What is VL and IL at 1?, 2?, 3?, 4?, and 5?? (Show this in a separate table.)

What is a time constant? What is a transient? What is the time constant ? for the circuit in Figure 7.1? What is the transient time for the circuit in Figure 7.1? What is the value of the current IL through the inductor at the beginning and the end of the charge cycle? What is the voltage VL across the inductor and the resistor at the beginning and the end of the charge cycle? How does the inductor act at the beginning and end of the charging process (short or open)? What is VL and IL at 1?, 2?, 3?, 4?, and 5?? (Show this in a separate table.)

Explanation / Answer

1)The time constant of an RL circuit is define as the time during which current would have reached its maximum value had it maintained its initial rate of rise. The expression for the time constant in an RL circuit is given by T = L/R

2)a transient is a part of solution that depens on time(t).

3)time constant=L/R=0.470/1000=0.470 mS

4)it is basically takes infinte time to reach steady state,Hence infinity.

5)Before switchig on the circuit the current was 0,The inductor resistors any change in corrent through it suddenly.Hence the current =0

6)Since the current is 0 initialy.The potential across resistor=iR=0*R=0

the potential across the inductor(V) can be found by applying loop law ie 10-iR-V=0

we know i=0

finally curent is 0.01A

hence V=10V(potential across inductor)

Finally,

inductor potential will be 0

resistance potential will be 10 volts.

7)inductor intially resists any change hence acts like a open circuit.and finally acts as open circuit finally

8)current=(10/1000)(1-e^(-t/(0.470*0.001)))=0.01

across the inductor=10e^(-t/(0.470*0.001))=10-

At 1sec,2 sec,3s,4,s,5s

ir has already reached the steady state

since time constant is small hence,

current=0.01A

vl=0

in all cases

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