Non-Ohmic Devices Some of the most interesting devices do not follow Ohm’s Law Diodes are devices that let current through one way much more easily than the other way Superconductors are cold materials that have no resistance at all They can carry current forever with no electric field

Power and Resistors The charges flowing through a resistor are having their potential energy changed Q Where is the energy going? The charge carriers are bumping against atoms They heat the resistor up V

Uses for Resistors You can make heating devices using resistors Toasters, incandescent light bulbs, fuses You can measure temperature by measuring changes in resistance Resistance-temperature devices Resistors are used whenever you want a linear relationship between potential and current They are cheap They are useful They appear in virtually every electronic circuit

Direct Current (DC) Circuits Circuit Basics These circuit elements and many others can be combined to produce a limitless variety of useful devices wire open switch closed switch 2-way switch Two devices are in series if they are connected at one end, and nothing else is connected there Two devices are in parallel if they are connected at both ends + – ideal battery 1.5 V 47 F capacitor 4.7 k resistor

Resistors in Parallel and in Series When resistors are in series, the same current must go through both of them The total voltage difference is The two resistors act like one with resistance When resistors are in parallel, the same potential is across both of them The total current through them is The two resistors act like one with resistance

Parallel and Series - Formulas Capacitor Resistor Inductor* Series Parallel Fundamental Formula * To be defined in a later chapter

The Voltage Divider Many circuits can be thought of as a voltage divider Intentionally or unintentionally What’s the voltage drop across each of the resistors? R1 + – E R2 The larger resistor gets most of the voltage + – 120 V If Mr. Curious has a resistance of 10 k and the light bulb has a resistance of 240 , how bright is Mr. Curious? Not very bright

Ideal vs. Non-Ideal Batteries Up until now, we’ve treated a battery as if it produced a fixed voltage, no matter what we demand of it Real batteries also have resistance It limits the current and therefore the power that can be delivered If the internal resistance r is small compared to other resistances in the problem, we can ignore it E + – ideal battery + – E r realistic battery A 30 V battery with 10  of internal resistance is connected to a 50  resistor. What is the actual voltage across the 50  resistor? + – 30 V 10  50 

Kirchoff’s Laws 12 V I1 Kirchoff’s Laws help us figure out where and how much current is flowing in a circuit The first step is to assign a direction and a current to every part of a circuit Items in series must have the same current in them Then you apply the two laws, which can be thought of as conservation of charge and conservation of voltage, which you apply to vertices and loops respectively. + – 3  I2 + – 5  6 V Kirchoff’s First Law: The total current into any vertex equals the current out of that vertex Kirchoff’s Second Law: The total voltage change around a loop is always zero 4  I3 These yield a series of equations, which you then solve