A circuit is constructed with four resistors one inductor on

A circuit is constructed with four resistors, one inductor, one battery and a switch as shown. The values for the resistors are: R₁ = R₂ = 36 , R₃ = 108 and R₄ = 95 . The inductance is L = 299 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 I_L(), 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(t_open), the current through the resistor R₃ at a time t_open = 3.3 ms after the switch was opened? The positive direction for the current is indicated in the figure.

A

5)

What is V_L,max(closed), the magnitude of the maximum voltage across the inductor during the time when the switch is closed?

V

6)

What is V_L,max(open), the magnitude of the maximum voltage across the inductor during the time when the switch is open?

V

Solution

1.

Immediately after switch is closed at t=0 ,inductor will act as open circuit .so current flowing in the circuit is

I=V/(R₁+R₃+R₄) =12/(36+108+95)

I=0.0502 A

Current through R4 is

I₄=I=0.0502 A

2.

After long time ,inductor will act as short circuit,so equivalent resistance

R_eq =36+95+36*108/(36+108)

R_eq = 158 ohms

So total current

I=V/R_eq = 12/158 =0.076 A

So current through R4 is

I₄=0.076

c)

Current through inductor is

I_L=I₂ =0.76*(108/108+36) =0.057 A

d)

Time Constant

T=L/(R₂+R₃)=0.299/(36+108)

T=2.08ms

For a discharging RL cirucit current as a funciton of time is given by

I=I_oe^-t/T

I =0.057*e^-3.3/2.08

I=0.0116 A