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 = 77 and R4 = 133 . The inductance is L = 295 mH and the battery voltage is v = 12 V. The positive terminal of the battery is indicated with a + sign. 2 1) The switch has been open for a long time when at time t - 0, the switch is closed. What is l4(0), the magnitude of the current through the resistor R4 just after the switch is closed? A Submit You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question 2) What is 14), the magnitude of the current through the resistor R4 after the switch has been closed for a very long time? A Submit You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question 3) What is L(), the magnitude of the current through the inductor after the switch has been closed for a very long time? A Submit

Explanation / Answer

As shown in the figure

Given, R1 = R2 = R = 56 ohms

R3 = 77 ohms

R4 = 133 ohm

Inductance, L = 295 mH

Battery voltage, V = 12 V

1. when the switch is closed, the induxtor acts as an open switch

so, R2 gets out of circuit

so then from ohms law

V = i4*(R1 +R3 + R4)

i4 = 12/(56+77+133) = 45.1127 A

2. when the switch is closed for a long time

the inductor acts as a short component

so, R2 and R3 become in parallel

Reff of the circuit, Reff = R1 + R2R3/(R2 + R3) + R4

Reff = 56 + 56*77/(56+77) + 133 = 221.42 ohm

so, V = i4*Reff ( from the circuit )

so, 12/Reff = i4 = 54.195 mA

3. Il = V/R2

Il = 12/56 =214.285 mA

4. when the switch is open

the inductor discharge equation is given by

Il = Iol*e^(-t*R/L)

where R = R3 + R2 = 77 + 56 = 133 ohms

Iol = 214.285 mA

so, Il = 214.285*(e^(-3.5*133/295)) = 44.227 mA

5. Vl,max is maximum when the switch is closed, at that point , Il = 0

so Vl,max = V = 12 V

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