Kirchoff’s Rules Kirchoff’s Junction Rule: at any junction point, the sum of all currents entering the junction must equal the sum of all currents leaving the junction. Also called Kirchoff’s First Rule.* Kirchoff’s Loop Rule: the sum of the changes of potential around any closed path of a circuit must be zero. Also called Kirchoff’s Second Rule. ** *This is just conservation of charge: charge in = charge out. **This is just conservation of energy: a charge ending up where it started out neither gains nor loses energy (E i = E f ).

19.4 Solving Problems with Kirchoff’s Rules Just as we had a litany for force problems in our Mechanics semester, we have a litany for circuit problems. Litany for Circuit Problems 1. Draw the circuit (if not already done). 2. Label + and – for each battery (the short side is -). 3. Label the current in each branch of the circuit with a symbol and an arrow. You may choose whichever direction you wish for the arrow. 4. Label junctions a,b,… Apply Kirchoff’s Junction Rule at each junction. The direction of the current arrows tell you whether current is flowing in (+) or out (-). Step 4 will probably give you fewer equations than variables. Proceed to step 5 go get additional equations.

5. Label loops A, B, … Apply Kirchoff’s Loop Rule for as many loops as necessary to get enough equations to solve for your unknowns. Follow each loop in one direction only—your choice. 5a. For a resistor, the sign of the potential difference is negative if your chosen loop direction is the same as the chosen current direction through that resistor; positive if opposite. 5b. For a battery, the sign of the potential difference is positive if your chosen loop direction moves from the negative terminal towards the positive; negative if opposite. 6. Collect equations, solve, and check results.

We need a shortened version of the litany for quick reference. 1. Draw the circuit. 2. Label + and – for each battery. 3. Label the current in each branch of the circuit with a symbol and an arrow. Label junctions a,b, … 4. Apply Kirchoff’s Junction Rule at each junction. Current in is +. Brief litany for Circuit Problems 5. Apply Kirchoff’s Loop Rule for as many loops (A,B…) as necessary. Follow each loop in one direction only. 5a. Resistor: + - I loop V is - 5b. Battery: loop V is + 6. Solve.

R2R2 R1R1 + - V I3I3 I2I2 I1I1 1. Draw the circuit. 2. Label + and – for each battery. 3. Label the current in each branch.* Label junctions a,b, … LOWERCASE! *There is MAJOR confusion regarding branches and loops. A junction is where two or more wires meet. A branch is a series-only circuit segment connecting two and only two junctions. Unless the circuit is a single loop and a single branch, loops have more than one branch in them. Currents are along branches only! ba 4. When you apply Kirchoff’s Junction Rule, do this! a: +(-I 1 ) +(-I 2 ) +(I 3 ) = 0

R2R2 R1R1 + - V I3I3 I2I2 I1I1 ba 5. Apply Kirchoff’s Loop Rule for as many loops as necessary. Follow each loop in one direction only. LABEL THE LOOPS A, B, C… Do this: A: +(I 2 R 2 ) +(-V) = 0 B A IMPORTANT: put your pen on the start of your loop. Manually trace around the loop. Every time you come to a circuit element, do this +(__) and fill the appropriate value in the blank! Continue until you reach the stopping point. If you label your junction equations a:, b:, etc. and your loop equations A:, B:, etc. you will avoid confusing your hapless instructor and likely prevent loss of points!