Pre-LAB 6 Preparation: Fundamentals of Circuits IV: Kirchhoff's ...

Fundamentals of Circuits IV: Kirchhoff’s Circuit Rules v 0.3In Fig. 8, the directions for the currents through the branches and for I 2 are assignedarbitrarily. If the internal resistances of the batteries are negligible, then by applying the loopand junction rules we find that:Loop 1: V 1 − I 2 R 2 − I 1 R 1 = 0 (1)Loop 2: −V 2 + I 2 R 2 + I 3 R 3 = 0 (2)And applying the junction rule gives usJunction 1: I 1 + I 3 = I 2 (3)It is not obvious that the loops and their directions can be chosen arbitrarily.Let’s explore this assertion theoretically for a simple situation and then more concretelywith some specific calculations. In order to do the following activity you’ll need a couple ofresistors and a multimeter as follows:• 1 carbon resistor, 39Ω• 1 carbon resistor, 68Ω• Circuit board with variable resistor• 1 multimeter• 1 battery, 6V• connecting wiresActivity 3.1: Applying the Loop and Junction Rules again.Fig. 9 shows the same circuit as Fig. 8, but with different choices of directions for the loops andcurrent through R 2 .I 1I 3R 3I 3++V 1 R 2V 2−−I 2I 1R 1Figure 9: A circuit identical to that in Fig. 8, but showing opposite direction for the loops, andopposite choice for the positive direction of current flowing through R 2 .Step 1: Use the loop and junction rules along with the new direction chosen for I 2 to rewritethe three equations relating values of battery voltages, resistance, and current in thecircuit shown in Fig. 9.PHYS-204:Physics II Laboratory 12