Need help in 4,5,and 6 A circuit is constructed with four resistors, one inducto

Question

Need help in 4,5,and 6

A circuit is constructed with four resistors, one inductor, one battery and a switch as shown. The values for the resistors are: R1-R2 = 24 , R3 = 114 and R4 = 135 . The inductance is L 259 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 14(0), the magnitude of the current through the resistor R4 just after the switch is closed? 0.043956 You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. Submit Your submissions: | 0.043956 Computed value: 0.043956 Feedback: Your answer has been judged correct; the exact answer is: 0.043956043956044 Submitted: Friday, March 16 at 3:25 AM 2) What is 14), the magnitude of the current through the resistor R4 after the switch has been closed for a very long time? 0.067104 You currently have 1 submissions for this question. Only 10 submission are allowed. Submit You can make 9 more submissions for this question. Your submissions: | 0.067104 Computed value: 0.067104 Feedback: Your answer has been judged correct; the exact answer is: 0.0671043034281545 Submitted: Friday, March 16 at 3:27 AM 3) What is L, the magnitude of the current through the inductor after the switch has been closed for a very long time? 0.055434 You currently have 1 submissions for this question. Only 10 submission are allowed. Submit You can make 9 more submissions for this question. Your submissions: 0.055434 Computed value: 0.055434 Feedback: Your answer has been judged correct; the exact answer is: 0.0554339897884755. Submitted: Friday, March 16 at 3:29 AM

Explanation / Answer

4) Max current through inductor is Imax = current through inductor after the switch has been closed for a very long time= 0.055434A

Now, the inductor is discharging, and current is given by I= Imax*e^(-Rt/L) ; where R= R2+R3= 24+114 = 138, t= 0.0041s, L= 0.259H

So, I3(topen)= 0.055434A * e ^ ( - 138 * 0.0041 / 0.259 ) = 6.23786 * 10^-3 A

5) Magnitude of max voltage across the inductor during the time when the switch is closed, is at t= 0 when the swich is just closed. At this time, the voltage across L and R2 is same as that across R3. All voltage across the branch with L and R2 is dropped in L which is, V= I4(0)*R3= 0.043956*114 = 5.010984V

So, VL,max(closed)= 5.010984V

6) Now, the max voltage across the inductor when the switch is open is when the switch is just opened. The voltage is same as the VL,max(closed) but in opposite direction. So, VL,max(open) = 5.010984V.

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