Problem In The Circuit Shown Notices That The Values Of Some Currents Are Given So That Instead Of Unknown Currents 1 (266.2 KiB) Viewed 121 times
Problem: In the Circuit shown, notices that the values of some currents are given, so that instead of unknown currents, the unknowns are the emf's ξ1 and ξ2, and the value of the resistor R, and the current through the 3Ω resistor. Four unknowns need four equations for a solution. Carefully write down the Kirchoff circuit laws for this problem and show your work as you solve for the unknown values. Input your answers into the Online Homework Ch24_Ex_6_Kirchoff quiz by tomorrow and 10:00 AM and turn in your work for this problem. (Hint: I used three small loops and the node beneath the 3 Ohm resistor.
Problem 2: The capacitor in the figure is initially uncharged. At t=0, a switch (not shown) is closed connecting the battery ξ through the rest of the circuit through R1. Find the time at which the voltage across the capacitor reaches half of its maximum value. Turn in your solution with your work. Input your answer online. (Hints: Use two simple Kirchoff loops and one node for the currents going through R1, R2 and R3, remembering that I3=dtdq the current into the capacitor, and that the voltage drop across the capacitor at any time is CQ(t). You will have three equations in the unknowns, I1,I2 and I3. Use ordinary algebra and two the equations to solve for and eliminate I1 and I2 symbolically, leaving only a single equation involving q and I3. Put this in the form of the equation dtdQ+RC1Q=ξ and read off the RC time, and the final voltage across the capacitor. Then use the equation V(t)=ξ(1−e−t/RC) to find the time the voltage is equal half its maximum value. ... I find that the maximum value is 18 volts.)
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