Ohm’s Law, Energy, Power, Series and Parallel Circuits Circuits 1 Fall 2005 Harding University Jonathan White

Outline ► Ohm’s Law  Georg Ohm  Relationship between resistance, current, and voltage ► Energy ► Power  In general  In electrical circuits ► Series and parallel circuits

Georg Simon Ohm ( ) ► German physicist who experimentally determined that the if the voltage across a resistor is increased, the current through the resistor will increase. ► Ideas were published in 1827, but they were rejected by his peers. He lived in poverty for several years before taking a teaching position. ► Called the Mozart of electricity.

Ohm’s Law ► V = I * R  For a constant resistance, if the current increases, the voltage increases at the same rate ► I = V / R  For a constant resistance, if the voltage increases, the current will increase at the exact same rate ► R = V / I  For a constant resistance, if the voltage increases, the current must increase at the exact same rate. ► Using the water pipe example, for a given size of valve (R), if you increase the pressure at which you push the water through the pipe (V), the amount of water that flows through the pipe will increase at the same rate(I).

Energy ► Energy is the fundamental capacity to do work. ► A charge can have potential energy (voltage) because of its place in space. ► In a power station, gas, coal, or nuclear energy is transformed into electrical energy – much like a battery. ► Note that energy can neither be created or destroyed, only transformed. ► Energy is measured in joules and symbolized by the letter w. (lowercase w). ► Energy is the amount of power consumed over time, which can be written as w=∫p dt from t 0 to t

Power ► Power is the rate at which energy is used. ► p = dW/dt, where W is energy and t is time  Since i=dq/dt and v = dw/dq, p can be rewritten as (dw/dq) * (dq/dt)  p=v*I ► Power in electrical circuits is measured in watts and symbolized by the letter W. Note: energy uses a lowercase letter and power uses an uppercase.  For example, a 60 watt light bulb uses 60 joules of energy in 1 second.

Power in Circuits ► Consider a device with a voltage across it and a current through it.  The voltage is a measure of the potential energy that a unit charge dissipates when it passes through a device. If the device is a resistor, then the energy lost will appear as heat.  The current is the number of charges that flow through a device in 1 second. ► If each couloumb dissipates V joules, and I couloumbs flows in one second, then the rate of energy dissipation is the product, VI.  That’s what power is, the rate at which energy is consumed.

Power Formulas ► P = VI  Note: Power can be negative. If the device is a battery, it is losing power so that the loads can do work. Can the power ever be negative for a resistor? By convention, if the current enters through the positive terminal of an element, the power is positive. If the current leaves an element (enters through the negative terminal), it is producing power, and the power will be negative. ► Using Ohm’s Law, you can state the above formula in a number of ways:  P = I 2 * R  P = V 2 / R

Energy Conversion in a resistor ► The power consumed by a resistor can be written as w=∫v*i dt from t 0 to t, since p=v*i. ► As you’ve seen, when there is a current through a resistance, electrical energy is converted to heat energy. ► This heat is caused by the collisions of the free electrons within the atomic structure of the resistive material. ► When a collision occurs, heat is given off and the electron gives up some of its acquired energy as it moves through the material.

Review ► Ohm’s Law:  V= I * R; I = V/R; R = V*I ► Energy  Definition: Capacity to do work.  Measured in joules.  Symbol is w  Energy can neither be created or destroyed, only transformed.  A battery stores energy

Review ► Power:  Definition: The rate at which energy is used.  Measured in watts.  Symbol is W.  P = W / t  In electrical circuits, ► P = V * I, P = I 2 * R, P = V 2 / R  Power can be negative, if something is supplying power. ► Voltage drops: Charge loses energy as it travels through circuits.