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 = 56 , R3 = 45 and R4 = 91 . 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 I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?

_______A

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

3)

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

______V

4)

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

___________A

5)

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

_______________A

Explanation / Answer

1)

just after the switch is closed, the inductor behaves as open circuit

hence Rtotal = total resistance = R1 + R2 + R3 + R4 = 56 + 56 + 45 + 91 = 248 ohm

V = battery Voltage = 24 Volts

i1 = current in R1 = V/Rtotal = 24/248 = 0.097 A

2)

long time after the switch is closed, the inductor behaves as short circuit

hence Rtotal = total resistance = R1 + R4 = 56 + 91 = 147 ohm

V = battery Voltage = 24 Volts

i1 = current in R1 = V/Rtotal = 24/147 = 0.163 A

3)

just after the switch is closed, the inductor behaves as open circuit

hence Rtotal = total resistance = R1 + R2 + R3 + R4 = 56 + 56 + 45 + 91 = 248 ohm

V = battery Voltage = 24 Volts

i = current in circuit = V/Rtotal = 24/248 = 0.097 A

VL = Voltage across indutor = Voltage across the series combination of R2 and R3 = i (R2 + R3) = (0.097) (56 + 45)

= 9.8 Volts

4)

long time after the switch is closed, the inductor behaves as short circuit

hence Rtotal = total resistance = R1 + R4 = 56 + 91 = 147 ohm

V = battery Voltage = 24 Volts

i1 = current in R1 = V/Rtotal = 24/147 = 0.163 A

iL = current in inductor = i1 = 0.163 A

5)

just after the switch is closed, the inductor behaves as open circuit

hence Rtotal = total resistance = R1 + R2 + R3 + R4 = 56 + 56 + 45 + 91 = 248 ohm

V = battery Voltage = 24 Volts

i1 = current in R1 = V/Rtotal = 24/248 = 0.097 A

i2= i1 = 0.097 A

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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