Ch 181 Chapter 18 © 2006, B.J. Lieb Some figures electronically reproduced by permission of Pearson Education, Inc., Upper Saddle River, New Jersey Giancoli, PHYSICS,6/E © 2004.

Ch 182 Simple Electric Cell Sulfuric acid Zn ______ Carbon Electrode (+) Zn Electrode (-) Two dissimilar metals or carbon rods in acid Zn + ions enter acid leaving terminal negative Electrons leave carbon making it positive Terminals connected to external circuit ‘Battery’ referred to several cells originally

Ch 183 Electric Current If we connect a wire between the two terminals electrons will flow out of the negative terminal and toward the positive terminal  we have an electric current. Electric current I is defined as the net amount of charge that flows past a given point per unit time. 1 C/s = 1A (ampere) An ampere is a large current and often currents are mA (10 -3 A) or  A (10 -6 A).

Ch 184 Electric Circuit It is necessary to have a complete circuit in order for current to flow. The symbol for a battery in a circuit diagram is: + _ Device +

Ch 185 “Conventional” current direction is opposite to actual electron flow direction which is – to +.

Ch 186 Ohm’ Law For wires and other circuit devices, the current is proportional to the voltage applied to its ends: I  V The current also depends on the amount of resistance that the wire offers to the electrons for a given voltage V. We define a quantity called resistance R such that V = I R (Ohm’s Law) The unit of resistance is the ohm which is represented by the Greek capital omega (  ). Thus

Ch 187 Resistors A resistor is a circuit device that has a fixed resistance. Resistor Circuit symbol Resistors obey Ohm’s law but not all circuit devices do. I V0 I V0 Resistor non-ohmic device

Ch 188 Example 18-1A. A person experiences a mild shock if a current of 80  A flows along a path between the thumb and the index finger. The resistance of this path is 4.0x10 5  when the skin is dry and 2000  when the skin is wet. Calculate the minimum voltage difference between these two points that will produce a mild shock.

Ch 189 Example 18-1B. Calculate the number of electrons per second that flow past a point on the skin in problem 18-1A.

Ch 1810 Resistivity In most electronic circuits we ignore the resistance of the wires because it is small in comparison to the other circuit components If we need to calculate the resistance of a given wire we can use its resistivity (  ) which is defined by: where L is the length of the wire and A is the cross sectional area. A L

Ch 1811 Resistivity and Temperature

Ch 1812 Resistivity and Temperature Resistivity usually depends on temperature. For most metals the resistivity increases with temperature. Often the flow of current through a wire is the cause of the temperature change. where T 0 is usually 20 o and  0 is the resistivity at that temperature.

Ch 1813 Example 18-2A A 35.0-m length of cooper wire has a radius of 0.25mm. Calculate the current in the wire if a potential difference of 9.0 V is applied across the length if the wire when the temperature is 20˚C. [for cooper ρ = 1.68×10 -8 Ωm and α = (˚C) -1 ]

Ch 1814 Example 18-2(B) If the wire in Example 18-2A is heated to 30˚C, what is the resulting current if the voltage difference is 9.0 V? Since R α ρ, we can see that: Gives:

Ch 1815 Superconductivity Materials require liquid helium for cooling. Since 1987 a new class of “high T C ” materials have been discovered that are superconducting up to 160 K. Would be many practical applications if some of the difficulties can be overcome. The resistivity of certain metals and compounds becomes zero at low temperatures near absolute zero- this state is called superconducting. Occurs only below a critical temperature TC which is usually close to absolute zero

Ch 1816 Power in Electric Circuits Electrical circuits can transmit and consume energy. When a charge Q moves through a potential difference V, the energy transferred is QV. Power is energy/time and thus: and thus:

Ch 1817 Notes on Power The formula for power applies to devices that provide power such as a battery as well as to devices that consume or dissipate power such as resistors, light bulbs and electric motors. For ohmic devices, the formula for power can be combined with Ohm’s Law to give other versions:

Ch 1818 Household Power Electric companies usually bill by the kilowatt-hour (kWh.) which is the energy consumed by using 1.0 kW for one hour. Thus a 100 W light bulb could burn for 10 hours and consume 1.0 kWh. Electric circuits in a building are protected by a fuse or circuit breaker which shuts down the electricity in the circuit if the current exceeds a certain value. This prevents the wires from heating up when carrying too much current.

Ch 1819 Connection of Household Appliances

Ch 1820 Example 18-3 (A) A person turns on a 1500 W electric heater, a 100 W hair dryer and then a 300 W stereo. All of these devices are connected to a single 120 V household circuit that is connected to a 20 A circuit breaker. At what point will the circuit breaker trip off?

Ch 1821 Example 18-3 (B) If electricity costs $0.12 per kWh., calculate the cost of operating all the appliances in the above problem for 2.0 hours.

Ch 1822 Alternating Current Electrical power is distributed using alternating current (ac) in which the current reverses direction with a frequency of 60 Hz (in the USA).

Ch 1823 Alternating Current The current and voltage varies as a sine function as shown above. Thus

Ch 1824 Average Power Even though the electron motion in ac circuits is back and forth they can still deliver power. Because the current and voltage change greatly over a cycle, we have to average over a cycle to get an accurate value for the average power consumed in the circuit

Ch 1825 Average Power The correct way to calculate this average is to use calculus to average the square of the current over a cycle and then take the square root of the result. This is called a root-mean-square (rms) average:

Ch 1826 Alternating Current/Voltage in U.S. In the U.S.: f = 60 Hz V 0  170 V V rms  120 V In Europe: f = 50 Hz V 0  310 V V rms  220 V

Ch 1827 Example 18-4 (A) A heater coil connected to a 240-V ac line has a resistance of 34 Ω. What is the average power used? (B) What are the maximum and minimum values of the instantaneous power?

Ch 1828 Microscopic View of Current Read Example It studies a 5.0A current in a copper wire that is 3.2 mm in diameter. It finds that the average “free” electron moves with a velocity of 4.7 x m/s in the direction of the current. This is called the drift velocity. It also assumes the “free” electrons behave like an ideal gas and calculates that the thermal velocity of the average electron is 1.2 x 10 5 m/s. Thus in a wire carrying a current, the electron motion is largely random with a slight tendency to move in the direction of the current. Thus if you could see electrons in a wire carrying current they would appear to be moving randomly.

Ch 1829 Summary of Units