Question

please help with problems 7 and 8, I am extremely confused!

Part 2: Kirchhoff's Rules For the circuit shown below, the directions of the currents through the circuit elements has been chosen arbitrarily. Using Kirchhoff's rules, you will determine the actual currents through the circuit elements. (Yes, this circuit could be analyzed using equivalent resistance, but don't do it that way.) R1: 752 Kirchhoff's Junction Rule 4) Start by choosing a junction. Write Kirchhoft's Junction rule for that junction below as equation 1. РАТНА Eq1: I. = I2 +I3 72 Kirchhoff's Voltage Rule (or loop rule) 5) Now before shrinking yourself down you must identify a R2 39.12 R3: 39.62 starting point and a path to walk around the circuit that PATHB B brings you back to the starting point R4 = 512 a) On the figure, label your starting point "A" b) Draw your path (the loop you intend to walk that returns you to your starting point) and label it "path A". c) Don't forget to indicate the direction you intend V1 = 3.0 V walking around this loop. d) Walk your chosen loop and use the rules for batteries and resistors to determine whether the voltage changes you encounter are positive or negative voltages changes. Write down all voltage rises and drops (adding them up) and set them equal to zero. Do this symbolically, no numbers. This is equation 2. Eq. 2: IR+I2 R2 + IZ R3 = 0 w 6) Do this a second time using a different starting point. a) On the figure, label your starting point "B" b) Draw a new path (the loop you intend to walk that returns you to your starting point) and label it "path B". c) Don't forget to indicate the direction you intend walking around this loop. d) Walk your chosen loop and write down all voltage rises and drops (adding them up) and set them equal to zero. Do this symbolically, no numbers. This is your third equation. Eq. 3: IzRz +IzR3 -I3 Ry + V, -O 4

Answer 1

Do not get confused while applying Voltage rule

Look at Path A here there is no voltage source in the loop

Voltage is dropped in all the resistances therefore all the voltage drops will have negative sign

this will lead to following equation

-I₁R₁ - I₂R₃ - I₂R₂ = 0

In Path B as you start from voltage source take it as Positive as you move and as you are moving against direction of I₂ the drop across R₂ and R₃ is positive. This will lead to following equation

V₁ + I₂R₃ + I₂R₂ - I₃R₄ = 0

(Note: If the direction of I₂ was opposite to the given direction then the drop will be negative as current direction then will be in same direction as we move, you can observe voltage drop across R₄ is negative as the current through R₄ which is I₃ is in same direction of path B)