1. Internal Resistance Review Kirchhoff’s Rules DC Electricity

2. Internal Resistance There is resistance to the flow of charge in a battery. This resistance is called internal resistance. A battery can therefore be considered to be a source of electromotive force (emf) connected in series with a resistor. The voltage measured over the terminals of the battery is called the terminal voltage. Note: the emf of a battery remains constant (e.g. 1.5 V for a D cell). However, when there is a current flowing, the terminal voltage changes because of the internal resistance.

3. From Your Data Data and Graph

4. Review Problem A battery has an EMF of 12.0 V and an internal resistance of 0.05 Ω. Its terminals are connected to a load resistance of 3.00 Ω. Find the current in the circuit and the terminal voltage of the battery. As a battery ages, its internal resistance increases and its ability to deliver energy to a load decreases. What would be the terminal voltage of the same battery with the same load connected if its internal resistance were 2.00 Ω.

5. Kirchhoff’s Rules The sum of the currents entering any junction must equal the sum of the currents leaving that junction. The sum of the changes in potential across all of the elements around any closed circuit loop must be zero.

6. Kirchhoff’s Current Law The sum of all currents flowing into a junction must equal the sum of the currents leaving the junction. Note that each branch in a circuit can have a different current.

7. Kirchhoff’s Voltage Rule To apply this rule, we imagine travelling around a circuit and consider changes in electric potential as we traverse the components in the circuit. For example, in a simple circuit containing an ideal battery (i.e. no internal resistance) and a resistor, the potential gained as we traverse the battery is lost as we traverse the resistor.

8. Kirchhoff’s Voltage Rule: Sign Conventions If a resistor is traversed with the current, there is a drop in electric potential (charges have more energy before they have passed through the resistor). If a resistor is traversed against the current, there is an increase in electric potential. If a source of EMF is traversed in the direction of the current there is a gain in electric potential (a battery “pushes” in this direction – therefore energy is added to charges). If a source of EMF is traversed in the direction opposite to the current, there is a drop in electric potential (going against the “push” of a battery).

10. Worked Example: Kirchhoff’s Rules In the single-loop circuit pictured, use Kirchhoff’s voltage law to determine the current flowing in the circuit. If we change the polarity of the 12V battery, what effect will this have on the current?

11. Worked Example 2: Multi-loop Circuit Work out the three unknown currents in this multi-loop circuit by using the current and voltage laws. Do now: write down three independent equations using the current and voltage rules.

12. Homework: Complete Electricity Worksheet 1 in your manuals. Due on Thursday.

13. Kirchhoff’s Voltage Law Challenge Problem Find the unknown currents in the following circuit:

14. Next Time: Applying Kirchhoff’s Rules to solve circuit problems