1. Aim: How can we use Kirchoff’s Rules to Analyze a circuit?
HW: Problem Set

2. Solve for the unknown current and Power across each resistor!
Break down and redraw the circuit piece by piece! Do NOT rush and simplify quick!

3. V I R P R1 R2 R3 R4 Req Pay attention to your rules! 20 Ω 30 Ω 50 Ω
0.58 W
0.17 A
3.19 V
0.11 A
0.35 W
3.19 V
0.06 A
0.2 W
Solve for Req
Solve for total current
Solve for individual Resistors starting with R1
Total current flows through combination R2 and R3. Solve for Voltage through Combo, which equals voltage through each one.
Solve for individual current through R2 and R3
3.4 V
0.17 A
0.58 W
0.17 A
58.75 Ω
1.7 W

4. Circuit Facts
Electromotive Force (EMF): Potential difference that drives flow of charge in a circuit.
This is NOT a force… fancy term for voltage (V)
Internal Resistance: Resistance across a battery.
What does this mean for the rest of the circuit?
Terminal Voltage: Effective voltage provided to the rest of the circuit.
An ideal battery has negligible resistance.

5. Kirchoff’s Rules
Sometimes a circuit is too complicated to solve by simple means…
Kirchoff’s Rules help us to easily analyze a circuit with multiple loops and batteries.
What does it mean for a circuit to have loops?
Loop: A closed path for a circuit.

6. Rule 1: Junction Rule
Total current into a junction must equal total current out.
IIN = IOUT
I1 = 0.5A
I2 = 2A
I3 = 1A
I4 = 3.5A I5 = ?

7. Rule 2: Loop Rule
The sum of the potential differences (positive and negative) that traverse any closed loop in a circuit must be zero.
Remember… V = IR
IT = I1
0 = I1R1 + I2R2 + I3R3
Remind students that battery does not have this shape and that if direction of current comes out of negative terminal, then we can take potential across battery to be negative with potential across resistors acting as positive if direction is kept constant.

8. Use Kirchoff’s Rules to determine current through R2 in the following circuit.
20 V
10 V
R2 = 20Ω
10 V
R1 = 10Ω
R3 = 30Ω
*Establish Junction Rule First, then Loop Rule.

9. Applying Kirchoff’s Rules
Junction Rule: I1+ I3 = I2
Loop 1: 0 = -20V + 10ΩI1+ 20ΩI2
Loop 2: 0 = -10V + 30ΩI3 + 20ΩI2
Using algebra solve for one current at a time!
Algebraic solution: Substitute in junction rule for I2. Then substitute equations into each other and solve for either I1 or I3.

10. Kirchoff Tricks
Choice of current direction when first starting the problem is arbitrary, just pick one and stick with it.
If direction comes out of negative battery terminal then potential is negative. Positive if directed out positive side.
Negative Current simply means direction is actually opposite what was taken.

11. Use Kirchoff’s Rules to determine current through R2 in the following circuit.
20 V
10 V
R2 = 20Ω
10 V
R1 = 10Ω
R3 = 30Ω
I2 = 0.64 A I3 = 0.08 A I1 = 0.72 A

12. Summary What does EMF stand for and represent?
What does it mean for a battery to have internal resistance? How does this relate to terminal voltage?
What are Kirchoff’s Rules?