ACTIVITY 1 (1st and 2nd Weeks): By Hand, DC Circuit Analysis On a sheet of regular paper, 8.5 x 11", design your own 2-loop (3 legs) DC circuit. It must contain 3 different resistors and 2 different batteries. Carefully label the battery polarities. The batteries must be on different legs and the resistors must also be on different legs. Of course, on two of the three legs there will be both a resistor and battery (in series). Assign arbitrary values to each element. As an example, the resistors could be: 30, 50, and 90 and the batteries: 3V and 8V. Assign an arbitrary variable for the current flowing in each leg, also choose an arbitrary (current) direction for each leg. As an example, the current in the first leg could be labeled: ia and flow upward, the current in the second leg could be labeled: i, and flow downward, etc. Using Kirchhoff's Voltage Law (twice, i.e. for two loops) and current conservation (applied at one of the nodes), write down the three equations that will allow you to solve for the three currents. Using techniques learned from your college math course(s), simultaneously solve the three equations for the three unknown currents (both the magnitude of the current in each leg and the direction of the current in the leg). Next, using Ohm's Law, determine the voltage drops across each resistor. Clearly label the polarity of the voltage drop. As an example, let's say the voltage drop across one of the resistors is 3 volts, clearly label which side of the resistor is positive and which side is negative. Finally, check your work. You now know the voltages across each element (resistors and batteries) in the circuit. Therefore, for two different loops, apply Kirchhoff's Voltage Law and show that when you sum the voltages around the loop, the sum is zero.