Ideal vs Real Battery Ideal battery: no internal energy dissipation Energy conservation Work done by battery is equal to energy dissipated in resistor EMF  = terminal voltage V Real battery: internal energy dissipation exists dW > i2Rdt or  > iR=V

Real Battery = Resistors in Series The current through devices in series is always the same. Req i ε terminal voltage internal resistance For multiple resistors in series:

Resistors in Parallel Generally, ••• Devices in parallel has the same potential drop Generally, •••

Kirchhoff’s Rules Kirchhoff’s Rule 1: Loop Rule When any closed loop is traversed completely in a circuit, the algebraic sum of the changes in potential is equal to zero. Coulomb force is conservative Kirchhoff’s Rule 2: Junction Rule The sum of currents entering any junction in a circuit is equal to the sum of currents leaving that junction. Conservation of charge In and Out branches Assign Ii to each branch

Kirchhoff’s Loop Rule Example When any closed loop is traversed completely in a circuit, the algebraic sum of the changes in potential is equal to zero. where is the potential difference across i-th device in the circuit: positive if potential rises negative if potential drops terminal voltage

Loop Example with Two EMF Devices IR1 IR2 ε2 Ir2 IR3 ε1 Ir1 If 1 <2, we have I<0 !? Þ This just means the actual current flows reverse to the assumed direction. No problem!

Finding Potential and Power in a Circuit But what is I? Must solve for I first! supplied by 12V battery Just means 0 V here dissipated by resistors The rest? into 4V battery (charging)

Charging a Battery Positive terminal to positive terminal Charging EMF > EMF of charged device battery being charged (11V) good battery (12V) Say, R+r1+r2=0.05 (R is for jumper cables). Then, power into battery 2 If connected backward, Large amount of gas produced Huge power dissipation in wires

Using Kirchhoff’s Laws in Multiple Loop Circuits Identify nodes and use Junction Rule: Identify independent loops and use Loop Rule: Only two are independent.

Circuit Analysis Tips Sketch the diagram Simplify using equivalent resistors Label currents with directions Use Junction Rule in labeling Choose independent loops Use Loop Rule Solve simultaneous linear equations

Another example (with parallel R combos) I1+I2 I2 Sketch the diagram Simplify using equivalent resistors Label currents with directions Use Junction Rule in labeling Choose independent loops Use Loop Rule Solve simultaneous linear equations I1 Replace by equivalent R=2 first.

Ammeter and Voltmeter Ammeter: an instrument used to measure currents It must be connected in series. The internal resistance of an ammeter must be kept as small as possible. Voltmeter: an instrument used to measure potential differences It must be connected in parallel. The internal resistance of a voltmeter must be made as large as possible.

Galvanometer Inside Ammeter and Voltmeter Galvanometer: a device that detects small currents and indicates its magnitude. Its own resistance Rg is small for not disturbing what is being measured. shunt resistor galvanometer Ammeter: an instrument used to measure currents Voltmeter: an instrument used to measure potential differences galvanometer