2/25/2014. Circuits. Properties of a Current. Conservation of Current. Definition of a Current A. I A > I B > I C B. I B > I A C. I C D. I A E.

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1 Circuits Topics: Current Conservation of current Batteries Resistance and resistivity Simple circuits 0.1 Electromotive Force and Current Conventional current is the hypothetical flow of positive charges that would have the same effect in the circuit as the movement of negative charges that actually does occur. Sample question: How can the measurement of an electric current passed through a person s body allow a determination of the percentage body fat? Properties of a Current Conservation of Current Definition of a Current Rank the bulbs in the following circuit according to their brightness, from brightest to dimmest. The wires below carry currents as noted. Rate the currents IA, IB and IC: A. I A B. I B C. I C D. I A E. I C 1

2 Batteries 0.3 Resistance and Resistivity The potential difference between the terminals of a battery, often called the terminal voltage, is the battery s emf. W V bat = chem = ε q L R = ρ A Simple Circuits Checking Understanding The current is determined by the potential difference and the resistance of the wire: I = V chem R A battery is connected to a wire, and makes a current in the wire. i. Which of the following changes would increase the current? ii. Which would decrease the current? iii. Which would cause no change? A. Increasing the length of the wire B. Keeping the wire the same length, but making it thicker C. Using a battery with a higher rated voltage D. Making the wire into a coil, but keeping its dimensions the same E. Increasing the temperature of the wire Resistivity The resistance of a wire depends on its dimensions and the resistivity of its material: 0.3 Resistance and Resistivity Impedance Plethysmography. L L L R = ρ = ρ = ρ A V L V calf calf

3 0. Ohm s Law Electric Blankets OHM S LAW The ratio V/I is a constant, where V is the voltage applied across a piece of material and I is the current through the material: V = R = constant or I V = IR 1. An electric blanket has a wire that runs through the interior. A current causes energy to be dissipated in the wire, warming the blanket. A new, low-voltage electric blanket is rated to be used at 18 V. It dissipates a power of 8 W. What is the resistance of the wire that runs through the blanket?. For the electric blanket of the above example, as the temperature of the wire increases, what happens to the resistance of the wire? How does this affect the current in the wire? The dissipated power? SI Unit of Resistance: volt/ampere (V/A) = ohm (Ω) 0.4 Electric Power Series Resistors Consider the charge q flowing through a battery where the potential difference between the battery terminals is V. energy power ( q) V q P = = V = IV t t time 0.4 Electric Power ELECTRIC POWER Parallel Resistors When there is current in a circuit as a result of a voltage, the electric power delivered to the circuit is: SI Unit of Power: watt (W) P = IV Many electrical devices are essentially resistors: P = I ( IR) = I R V V P = V = R R 3

4 Kirchhoff s Laws Measuring Body Fat The resistivity of the body is a good measure of its overall composition. A measure of the resistance of the upper arm is a good way to estimate the percent fat in a person s body. Let s model a person s upper arm as a cylinder of diameter 8.0 cm and length 0 cm. We can model the composition of the arm by assuming that the muscle, far, and nonconductive portions (the bone) form simple regions. This simple model actually works quite well. For a typical adult, the bone has a cross-sectional area of 1.0 cm ; to a good approximation, the balance of the arm is fatty tissue or muscle. A. Assume that the arm has 30% fat and 70% muscle. What is the resistance of the arm? B. Now, assume that the arm has only 10% muscle. What is the resistance now? The measurement of the resistance of the arm is made by applying a voltage and measuring a current. Too much current can be uncomfortable and, as we will see, can be dangerous. Suppose we wish to limit the current to 1.0 ma. For each of the above cases, what is the maximum voltage that could be employed? 0.6 Series Wiring 0.8 Circuits Wired Partially in Series and Partially in Parallel There are many circuits in which more than one device is connected to a voltage source. Series wiring means that the devices are connected in such a way that there is the same electric current through each device. 0.7 Parallel Wiring 0.11 The Measurement of Current and Voltage Parallel wiring means that the devices are connected in such a way that the same voltage is applied across each device. An ammeter must be inserted into a circuit so that the current passes directly through it. When two resistors are connected in parallel, each receives current from the battery as if the other was not present. Therefore the two resistors connected in parallel draw more current than does either resistor alone. 4

5 0.11 The Measurement of Current and Voltage To measure the voltage between two points in a circuit, a voltmeter is connected between the points. 0.7 Parallel Wiring 5