 # Current and Resistance

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Current and Resistance
Chapter 17 Current and Resistance Conceptual questions: 3,6,10,14 Quick quizzes: 1,3,4,5,6,7 Problems: 12,27,30,47

Electric Current The current is the rate at which the charge flows through a surface The direction of current flow is the direction positive charge would flow The SI unit of current is Ampere (A) 1 A = 1 C/s

QUICK QUIZ 17.1 Consider positive and negative charges moving horizontally through the four regions in Figure Rank the currents in these four regions, from lowest to highest.

Charge Carrier Motion in a Conductor
The zig-zag black line represents the motion of charge carrier in a conductor The net drift speed is small The sharp changes in direction are due to collisions The net motion of electrons is opposite the direction of the electric field

Electrons in a Circuit The drift speed is much smaller than the average speed between collisions Although the drift speed is on the order of 10-4 m/s the effect of the electric field is felt on the order of 108 m/s

Meters in a Circuit -- Ammeter
An ammeter is used to measure current In line with the bulb, all the charge passing through the bulb also must pass through the meter

Meters in a Circuit -- Voltmeter
A voltmeter is used to measure voltage (potential difference) Connects to the two ends of the bulb

QUICK QUIZ 17.3 Look at the four “circuits” shown below and select those that will light the bulb.

Resistance The resistance of the conductor
Units of resistance are ohms (Ω) 1 Ω = 1 V / A Resistance in a circuit arises due to collisions between the electrons carrying the current with the fixed atoms inside the conductor

Ohm’s Law; ohmic materials ΔV = I R
Ohm’s Law is an empirical relationship Materials that obey Ohm’s Law are said to be ohmic

Non-ohmic materials The current-voltage relationship is nonlinear
A diode is a common example of a non-ohmic device

QUICK QUIZ 17.4 In the figure below, does the resistance of the diode (a) increase or (b) decrease as the positive voltage ∆V increases?

Resistivity The resistance of an ohmic conductor is proportional to its length, L, and inversely proportional to its cross-sectional area, A ρ is the constant of proportionality and is called the resistivity of the material See table 17.1

Problem 17-12 Suppose that you wish to fabricate a uniform wire out of 1 g of copper. If the wire is to have a resistance of R=0.500 Q, and if all of the copper is to be used, what will be A. the length B. the diameter of that wire?

QUICK QUIZ 17.5 Aliens with strange powers visited Earth and doubled every linear dimension of every object on the surface of the Earth. A wire has the length and diameter twice their original values. Does the wire now have (a) more resistance than before, (b) less resistance, (c) the same resistance? (Assume the resistivities of materials remain the same before and after the doubling.)

Temperature Variation of Resistivity
For most metals, resistivity increases approximately linearly with temperature ρo is the resistivity at some reference temperature To To is usually taken to be 20° C  is the temperature coefficient of resistivity see Table 17.1

Temperature Variation of Resistance
Since the resistance of a conductor with uniform cross sectional area is proportional to the resistivity, the effect of temperature on resistance is

Problem 17-27 A 34.5 m length of copper wire at 20.0oC has a radius of 0.25 mm. If a potential difference of 9.0 V is applied across the length of the wire, determine the current in the wire. If the wire is heated to 30.0oC while the potential difference is maintained, what is the resulting current in the wire?

Solving for T gives the temperature of the melting potassium as
Problem 17-30 A platinum resistance thermometer has resistances of Ω when placed in a 0°C ice bath and Ω when immersed in a crucible containing melting potassium. What is the melting point of potassium? (Hint: First determine the resistance of the platinum resistance thermometer at room temperature, 20°C.) The resistance at 20.0°C is Solving for T gives the temperature of the melting potassium as

Superconductors A class of materials and compounds whose resistances fall to virtually zero below a certain temperature, TC TC is called the critical temperature The graph is the same above TC, but suddenly drops to zero at TC

Electrical Energy and Power
The rate at which the energy is lost is the power From Ohm’s Law, alternate forms of power are

Electrical Energy and Power
The SI unit of power is Watt (W) The unit of energy used by electric companies is the kilowatt-hour This is defined in terms of the unit of power and the amount of time it is supplied 1 kWh = 3.60 x 106 J

QUICK QUIZ 17.6 A voltage V is applied across the ends of a nichrome heater wire having a cross-sectional area A and length L. The same voltage is applied across the ends of a second heater wire having a cross-sectional area A and length 2L. Which wire gets hotter? (a) the shorter wire, (b) the longer wire, (c) not enough information to say.

QUICK QUIZ 17.7 For the two resistors shown here, rank the currents at points a through f, from largest to smallest.

Problem 17-47 The kilowatt-hour is a measure of energy equal to
The heating coil of a hot water heater has a resistance of 20 W and operates at 210 V. If electrical energy costs \$0.080/kWh, what does it cost to raise the 200 kg of water in the tank from 15 °C to 80 °C? The kilowatt-hour is a measure of energy equal to The energy needed to raise the temperature of 200 kg of water from 15 C ° to 80 C ° is and the cost of operating the heater to produce this quantity of thermal energy is (cost)= (energy used) (rate) = (15 kWh) (\$0.080/kWh) = \$1.20

Conceptual questions Why don’t the free electrons in a metal fall to the bottom of the metal due to gravity? Charges in a conductor are suppose to reside on the surface – why don’t the free electrons all go to the surface? 6. Two lightbulbs are each connected to a voltage of 120V. One has a power of 25 W, the other 100 W. Which bulb has a higher resistance? Which bulb carries more current? 10. Some homes have light dimmers that operate by rotating a knob. What is being changed in the electric circuit when the know is being rotated? 14. Use the atomic theory of matter to explain why the resistance of a metal should increase as its temperature increases.

In the two cases shown here a battery is connected up to a box containing some resistors. The battery provides an EMF =V0. Which box will draw more current from the battery? 1. They will draw the same amount. 2. #1 will draw twice as much as #2. 3. #1 will draw more than #2 but not twice. 4. #2 will draw twice as much as #1 5. #2 will draw more than #1 but not twice. 6. You can’t tell from the information given

MCAT A positive charge q=1.1x10-11 C is located 0.01 m away from a negative charge of equal magnitude. Point P is exactly between them. What is the magnitude of the electric field at point P? a N/C b N/C c N/C d N/C If a water molecule is placed between two plates of a capacitor, which orientation would it take to minimize its energy? The electric field is up. a. H b. H O O H H c. H H d. O O H H E

MCAT, cont. a. resistance b. capacitance
The ratio of the potential difference across a conductor and the current moving through it is called the a. resistance b. capacitance d. conductance d. electric potential In a solid metal conductor, electric current is the movement of a. electrons only b. protons only c. nuclei d. protons and electrons A 12 W load is connected across a 6.0 V battery. How much energy does the load use in ½ an hour? a. 1.5 x 10-3 kWh b. 2.0 x 10-3 kWh c. 3.0 x 10-3 kWh d. 12 x 10-3 kWh