A circuit is constructed with four resistors, one inductor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 48 Ω, R3 = 100 Ω and R4 = 130 Ω. The inductance is L = 330 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 I_{4}(0), the magnitude of the current through the resistor R_{4} just after the switch is closed?
2)
What is I_{4}(?), the magnitude of the current through the resistor R_{4} after the switch has been closed for a very long time?
3)
What is I_{L}(?), the magnitude of the current through the inductor after the switch has been closed for a very long time?
4)
After the switch has been closed for a very long time, it is then opened. What is I_{3}(t_{open}), the current through the resistor R_{3} at a time t_{open} = 5.6 ms after the switch was opened? The positive direction for the current is indicated in the figure.
5)
What is V_{L,max}(closed), the magnitude of the maximum voltage across the inductor during the time when the switch is closed?
6)
What is V_{L,max}(open), the magnitude of the maximum voltage across the inductor during the time when the switch is open?
Something we need to understand before solving the problem is that when we have an inductor and the problem have a switch that will be open/closed for long/short periods of time the inductor acts like a huge resistor that basically drains all the energy and dont let it flow when the switch is recently opened (t=0) and will act like a wire (as if it was not even on the picture) when the switch was opened a long time ago (t=infinity). This will help us solve some of the questions.
Question 1
To calculate the current in resistor 4 we have
And R_{T} is the sum of all the resistors, but, since t=0 no current will flow after the inductor so we ignore R_{2}
_{}
_{}
Question 2
Same as last question but this time we do consider R_{2} since the inductor is acting as just a wire (we ignore it)
Question 3
Again like last question the inductor acts like a wire so the current throught it will be the same as the current on R_{2} (because they are in series) so we basically need I_{2} as if there was no inductor there. In order to find it we need the voltage that is going on the second loop that splits (parallel) between R_{3} and R_{2} and the current for this case is the same as last problem since the conditions are the same
Now we calculate I_{2} since is the same current as the current in the inductor and remember that we calculated the voltage that goes to both R_{3} and R_{2} so V_{23}=V_{2}=V_{3}
Question 4
Now to find current with a certain specific time we go by:
I made it bigger so you can see it better. Now we need since I_{max} is the current we calculated before since is the current with the switch open for the maximum time and t is the given time (in seconds). We have then
And R is the sum of the resistors in the loop which are R_{2} and R_{3} and this time they are in series (only for this loop not the circuit) so we have
This is a complex number so i will keep it for the formula to avoid having a serious difference in the result due to using less significant numbers.
Is negative because it goes in the opposite direction as of what the problem says is positive
Question 5
For this question we have that
And since is max closed we take as if it were t=0 (same current as question 1) and the resistor R_{3} is parallel to the inductor the voltage in both of them will be the same and like i said in question 1 we ignore R_{2}, so we have.
Question 6
This time we follow the same procedure as last question but this time we have max open, so, we take the I from question 3 (same conditions) and the resistance now includes R_{2} so we need the total resistance R_{23} that are in parallel for this loop so we have
---------------------------------------------------------------------
This was a really long question, i hope you could understand everything.
---------------------------------------------------------------------
I'm glad I was able to help! Don't forget you can hit that thumbs up button for my work! I'll appreciate it. Thank you.
A circuit is constructed with four resistors, one inductor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 48 Ω, R3 = 100 Ω and R4 = 130 Ω.
A circuit is constructed with four resistors, one inductor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 49 Q, R = 105 Q and Ra = 142 . The inductance is L = 354 mH and the battery voltage is V = 12 V. The positive terminal of the battery is indicated with a + sign. "TII Luni 1) The switch has been open for a long time when at time...
A circuit is constructed with four resistors, one inductor, one battery and a switch as shown. The values for the resistors are: R1-R2-76 Ω, R3-105 Ω and R4-810. The inductance is L-478 mH and the battery voltage is V-24 V 1) The switch has been open for a long time when at time t - o, the switch is closed. What is 11(0), the magnitude of the current through the resistor R1 just after the switch is closed? A uIii...
A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 34 ?, R3 = 114 ? and R4 = 145 ?. The capacitance is C = 46 ?F 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 =...
answer all 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 Ω, R3-45 Ω and R4-91. The inductance is L-245 mH and the battery voltage is V- 24V 1) The switch has been open for a long time when at timet 0, the switch is closed. What is I1(0), the magnitude of the current through the resistor R1 just after the switch is closed? 2) What...
A circuit is constructed with four resistors, one inductor, one battery and a switch as shown. The values for the resistors are: R1 - R-410, R3 - 700 and Ry - 145 . The inductance is L-200 mH and the battery voltage is V-12 V. The positive terminal of the battery is indicated with a + sign. WW11 R L v The switch has been open for a long time when at time t - 0, the switch is closed....
A circuit is constructed with four resistors, one inductor, one battery and a switch as shown. The values for the resistors are: R = R2 = 622, R3 = 91 and R - 74 . The inductance is L-205 mH and the battery voltage is V - 24V. v + Lun lai 1) The switch has been open for a long time when at time t = 0, the switch is closed. What is 1(O), the magnitude of the current...
I4(0) ... current through R4 just after switch is closed ... = 0.04196 A I4(∞) ... current through R4 after switch has been closed for a very long time ... = 0.05539 A IL(∞) ... current through inductor after switch has been closed for a very long time ... = 0.03767 A VL,max(closed) ... maximum voltage across inductor during the time when switch is closed ... = 4.28 V VL,max(open) ... maximum voltage across inductor during the time when switch...
A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 60 Ω, R3 = 49 Ω and R4 = 133 Ω. The capacitance is C = 75 μF 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...
Two Loop RL Circuit1 A circuit is constructed with four resistors, one inductor, one battery and a switch as shown. The values for the resistors are: R1 R2-412, R3 70 and R4 64 . The inductance is L-422 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 10), the magnitude of the current through the resistor R1 just after...
A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 67 ?, R3 = 96 ? and R4 = 77 ?. The capacitance is C = 48 ?F and the battery voltage is V = 24 V. Consider the circuit above, with R5 = 67 ? in series with the capacitor. Once again, the switch has been open for a long time when at...