1) The switch has been open for a long time when at time t = 0, the switch is cl

Question

1)

The switch has been open for a long time when at time t = 0, the switch is closed. What is I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?

A

Your submissions:

2)

What is I1(), the magnitude of the current that flows through the resistor R1 a very long time after the switch has been closed?

A

Your submissions:

3)

What is VL(0), the magnitude of the voltage across the inductor just after the switch is closed?

V

Your submissions:

4)

What is IL(), the magnitude of the current through the inductor after the switch has been closed for a very long time?

A

Your submissions:

5)

What is I2(0), the magnitude of the current through the resistor R2 just after the switch is closed?

Explanation / Answer

1. When switch is closed,immediately the inductor behaves like an open circuit because it immediately sets up a voltage which opposes the battery voltage.

So in such condition the Circuit has effective resistance =R1 + R2 +R3+R4 = (47+47+76+67) Ohms

= 237 ohms

So Intial current = 24 Volts/237 ohms = 0.10 amperes

2. In this part we are required to find current in inductor after a very long time after switching circuit on. In such case inductance does not generate any opposing emf and hence acts just like any simple conductor and hence inductor behaves like a short circuit and hence , current bypasses the two resistors R2 and R3

So net resistance = R1+R4 =(47+67) ohms =114 ohms

Current = 24Volts/ 114ohms = 0.21 amperes

3. At the instant the switch is put on , the Inductor behaves as on open circuit and hence the voltage across it matches the battery voltage but is of opposite sign .This mean VL = - 24 V

4. In this part we are required to find current through inductor after very long time. By this time di/dt = 0 and hence steady state is acheived and hence inductor behaves as short circit and the current through it is same as current through R1 and R4 , that is 0.21 amperes

5. At the instant switch is closed inductor behaves as open circuit and hence current in R2 is same as current through all other resistors and hence is 0.10 amperes

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.