A circuit is constructed with four resistors, one inductor, one battery and a sw

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= 72 ?, R3= 57 ? and R4= 78 ?. The inductance is L = 667 mH and the battery voltage is V = 24 V.

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 R1just after the switch is closed?

I found this to be just I1(0)=Vb/Rtot=24/(72+72+57+78).

2)What is I1(?), the magnitude of the current that flows through the resistor R1a very long time after the switch has been closed?

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

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

5)What is I2(0), the magnitude of the current through the resistor R2just after the switch is closed?

Explanation / Answer

just after the switch is closed, inductor will act like open circuit so current in the loop=24/(72+72+57+78)=86 mA (1.)the magnitude of the current through the resistor R1just after the switch is closed=86 mA (2.) after very long time, inductor will act as short circuit. so current through R2 and R3 are zero. current through R1 and R4 =24/(72+78)=160 mA the magnitude of the current that flows through the resistor R1a very long time after the switch has been closed=160 mA (3.)the magnitude of the voltage across the inductor just after the switch is closed=i*(R2+R3)=0.086*(72+57)=11.094 volts (4.)the magnitude of the current through the inductor after the switch has been closed for a very long time=the magnitude of the current that flows through the resistor R1a very long time after the switch has been closed=160 mA (5) , the magnitude of the current through the resistor R2just after the switch is closed=86 mA

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