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: R_1 = R_2 = 64 Ohm, R_3 = 93 Ohm and R_4 = 75 Ohm. The inductance is L = 255 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 l_1(0), the magnitude of the current through the resistor R_1 just after the switch is closed? 2) What is l_1(infinity), the magnitude of the current that flows through the resistor R_1 a very long time after the switch has been closed? 3) What is V_L(0), the magnitude of the voltage across the inductor just after the switch is closed? 4) What is I_L(infinity), the magnitude of the current through the inductor after the switch has been closed for a very long time? 5) What is l_2(0), the magnitude of the current through the resistor R_2 just after the switch is closed?

Explanation / Answer

1. I_L = 0

so I_R1 = V / (R1 + R2 + R3 + R4)

= 24 / (64 + 64 + 93 + 75)

= 0.0811 A

2. after long time.

R2 and R3 will get short circuites by inductor coil.

I_R1 = V / (R1 + R4)

= 24 / (64 + 75)

= 0.173 A

3. VL = I (R2 + R3)

= 0.0811 (64 + 93)

= 12.7 Volt

4. IL = 0.173 A

5. I2 = 0.0811 A

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