AP Physics I Electric Current and Resistance Chapter

AP Physics I: Electric Current and Resistance

Chapter 17: Electric Potential, Energy, and Capacitance 17. 1 17. 2 17. 3 17. 4 Batteries and Direct Current and Drift Velocity Resistance and Ohm’s Law Electric Power

Warmup: Plugged In Daily Physics Warmup # 104 Electrical appliances can be found in practically every room of most homes in the modern world. They help us store and prepare food, provide entertainment, and allow us to live in a comfortable environment. What all of these appliances have in common is that they convert electrical energy into some other form of energy. ************************************* Fill in the blanks to identify four of the types of energy produced in electrical appliances. h E __ a __ t __ s __ o __ u N __ d __ m E __ c __ h __ a __ n __ i __ c __ a __ l __ R l __ i G __ h __ t __ Y

17. 1: Batteries and Direct Current

battery - a device that converts chemical potential energy into electrical energy. • Allesandro Volta constructed one of the first practical batteries. • He used zinc and copper electrodes in a weak sulfuric acid solution. circuit - any complete loop consisting of wires and electrical devices ex: batteries and light bulbs. anode (+) - the positive terminal of a battery. cathode (-) - the negative terminal of a battery. electric current - the net rate at which charge flows past a given point. direct current (dc) - in a battery circuit, the electrons can only flow in one direction, from negative terminal to positive terminal.

A Simple Chemical Battery: A battery consists of two electrodes (different metal strips) in an electrolyte (solution that conducts electricity). • The different metals dissolve at different rates in the acid. As the metals dissolve, their atoms move into solution as positively charged ions, leaving behind electrons. • Both electrodes accumulate excess electrons, but one will have a larger excess. The cathode becomes more negatively charged than the anode. The anode is at a higher potential than the cathode. • The potential difference across the electrodes can cause electrons to flow in the wire. In other words, the voltage causes current, or flow of charge, in the wire. There is also a current in the solution as the positive ions migrate, so the circuit is complete. • Over time, as electrode A continues to receive more electrons than normal, it attracts A ions from solution. A ions reattach to electrons to form neutral atoms and deposit on the A electrode. In the mean time, B is slowly dissolving. The chemical potential energy is converted to light and heat in the lightbulb.

electromotive force (emf) - the potential difference across the two terminals of a battery (or any dc power supply) when not connected to an external circuit. • emf is NOT a force; it is a voltage, measured in volts.

terminal voltage - is the voltage across a battery or power supply when it is connected to an external circuit. • Also called operating voltage • Terminal voltage is always less than the emf because of internal resistance of the battery. • A battery’s internal resistance depends on its age, type of electrolyte, and electrode material. • The terminal voltage is what a battery actual delivers; it can be considerably less than the emf.

V = - Ir (add to your gold sheet) terminal voltage = emf – (current) x (internal resistance of the battery) Example: A battery has an emf of 8. 40 V and an internal resistance of 0. 5 . It can supply a current of 0. 084 A. What is its terminal voltage? V = - Ir = 8. 40 V – (0. 084 A) (0. 5 ) = 8. 36 V

Batteries in Series • Notice the symbol for battery and resistance. A resistance is anything in the circuit that opposes the charge flow. • When batteries are connected in series, their voltages add and the voltage across the resistance R is the sum of the voltages. • Example: Car batteries. These generally consist of six 2 -volt cells connected in series.

Batteries in Parallel • When batteries of the same voltage are connected in parallel, the voltage across the resistance is the same, as if only a single battery were present. • In this arrangement, each battery supplies a fraction of the total current. • Example: jumping your car. The strong battery (low resistance) delivers most of the current to help the weak battery (high resistance).

17. 2 Current and Drift Velocity

complete circuit - a battery or some other source connected to a continuous conducting path • To sustain electric current, a voltage source and a complete circuit is required. conventional current - the direction in which positive charge would move. • This is the historical or conventional way to analyze circuits • In most materials (e. g. , metals), the actual current is carried by electrons moving in the opposite direction to the conventional current due to the fact that electrons have negative charge.

electric current (I) – the time rate of flow of net charge I=q t current On Gold Sheet where q is the net charge that passes through a cross-sectional area of a wire at a given point in time t at a constant rate. • the SI unit of current is coulomb/s (C/s) or ampere (A), or “amps” for short • named after Andre Ampère (1775 -1836), an early investigator of electrical and magnetic phenomena

drift velocity - the average velocity of the electron flow in a metal wire. • much smaller than the random velocities of the electrons themselves. • drift velocity is approximately 1 mm/s • drift velocity is opposite the direction of the electric field, towards the positive terminal of the battery. • The electric field, which is what pushes the charges in the wire, travels down the wire at close to the speed of light (on the order of 108 m/s). • This is why the current starts “instantly” in all parts of the circuit.

Example 17. 1: If 3. 0 x 1015 electrons flow through a section of a wire of diameter 2. 0 mm in 4. 0 s, what is the electric current in the wire?

Check for Understanding 1. When a battery is placed into a complete circuit, the voltage across its terminal is its a) emf b) terminal voltage c) power d) all of these Answer: b 2. As a battery gets old, its a) emf increases b) emf decreases c) terminal voltage increases d) terminal voltage decreases Answer: d

Check for Understanding 3. When four 1. 5 volt batteries are connected in parallel, the output voltage of the combination is a) 1. 5 V b) 3. 0 V c) 6. 0 V d) none of these Answer: a 4. The unit of electrical current is a) C b) C/s c) A d) both b and c Answer: d

Warmup: Lighter Electric Bills Daily Physics Warmup # 79 Electric light bulbs come with various power ratings, such as 60 W and 100 W. Since light bulbs are used to produce light, it might seem logical that all light bulbs with the same power rating would produce the same amount of light. However, the power rating refers to how much energy is being used each second. Some of that energy is converted to heat as well as light and varies significantly depending on the nature of the bulb. ********************************************** Incandescent bulbs produce a lot more heat than fluorescent bulbs and therefore use more power to produce the same amount of light. The savings in cost to operate fluorescent bulbs can be quite surprising. It typically costs about 0. 007¢ per watt to operate something electrically for one hour. A 60 W incandescent bulb and a 15 W fluorescent bulb give off the same amount of light. Calculate the amount saved over a year’s time if they were used an average of 10 hours per day. Answer: $ 11. 50

17. 3 Resistance and Ohm’s Law

resistance (R) R= V I - the ratio of the voltage to the resulting current or V = IR Ohm’s Law On Gold Sheet • The SI unit of resistance is the volt per ampere (V/A) or ohm ( ). ohmic - a resistor is said to be ohmic if it has constant resistance. • Not all materials are ohmic: example: lightbulbs, semiconductors

Example 17. 2: A resistor with a resistance of 20 is connected to a 12 -volt battery. What is the current through the resistor?

Factors That Influence Resistance • The major factors that influence resistance of a conductor of uniform crosssection are: 1) the type of material or the intrinsic resistive properties 2) its length (L) 3) its cross-sectional area (A) 4) its temperature (T) Resistivity ( ) • determined by the resistive properties of a material (partly due to intrinsic atomic properties) R= L A or = RA L On Gold Sheet where R is resistance • the SI unit of resistivity is the ohm-meter ( · m)

conductivity ( ) – the inverse of resistivity =1 • the SI unit of conductivity is 1/ohm-meter [( ·m)-1]

Example 17. 3: Calculate the current in a piece of 10. 0 m long 22 -gauge (the radius is 0. 321 mm) nichrome wire if it is connected to a source of 12. 0 V. Assume the temperature is 20°C.

Check for Understanding 1. The unit of resistance is the a. V / A b. A / V c. W d. V Answer: a 2. For an ohmic resistor, current and resistance a) vary with temperature b) are directly proportional c) are independent of voltage d) none of these Answer: d (ohmic resistors have constant resistance by definition)

Check for Understanding 3. If voltage (V) were plotted on the same graph versus current (I) for two ohmic conductors with different resistances, how could you tell the less resistive one? Answer: Since V = R I (y = mx) , the one with the smaller slope is less resistive.

Check for Understanding

Warmup: Power Up! Daily Physics Warmup #77 Power is the rate at which energy is used. When an appliance is labeled with a certain power, such as 1, 200 watt hair dryer, it means that during each second of operation the dryer transforms 1, 200 joules of energy from one type of energy into other types of energy. ************************************ Identify the type of energy that operates the appliance and the type or types of energy it produces. Device toaster Energy In electrical Energy Out heat (light) portable generator chemical electric dryer electrical heat flashlight Electrical or chemical light (heat)

17. 4 Electric Power

P = W = UE = q V t t t and since I = q, t • The SI unit of power is the watt (W). P= I V On Gold Sheet

joule heat – thermal energy expended in a current-carrying resistor • also known as I 2 R losses (“I squared R” losses) • can be undesirable (ex: electrical transmission lines) • can be the intended purposes (ex: hair dryers, toasters) • heat = power time (J/s s = J) kilowatt-hour (k. Wh) – a unit of work (energy) 1 k. Wh = (1000 W)(3600 s) = ( 1000 J/s)(3600 s) = 3. 6 x 106 J

Example : What amount of heat is generated in a 10 resistor that carries 0. 3 A of current for 3 minutes?

Example 17. 5: What is the operating resistance of a 100 W household light bulb? The operating line voltage of household electricity is 120 V.

Example 17. 6: A computer, including its monitor, is rated at 300 W. Assuming the power company charges 10 cents for each kilowatt-hour of electricity used and the computer is on 8. 0 hours per day, estimate the annual cost to operate the computer.

Check for Understanding 1. Electric power has units of a) b) c) d) A 2· J/s V 2/ all of these Answer: d 2. If the voltage across an ohmic resistor is doubled, the power expended in the resistor a) increases by a factor of 2 b) increases by a factor of 4 c) decreases by half d) none of these Answer: b, since P=V 2/R

Check for Understanding 3. If the current through an ohmic resistor is halved, the power expended in the resistor a) increases by a factor of 2 b) increases by a factor of 4 c) decreases by half d) decreases by a factor of 4 Answer: d, because P = I 2 R 4. Assuming your hair dryer obeys Ohm’s law, what would happen if you plugged it directly into a 240 -volt outlet in Europe if it is designed to be used in the 120 -volt outlets of the US? Answer: Since P = V 2/R, its power output would quadruple, and it would overheat at least.

Chapter 17 Formulas V = - Ir Defines terminal voltage in terms of emf, current, and internal resistance of a battery. I=q t Define electric current in terms of charge flow. V = IR Ohm’s Law. R= L A Defines the resistivity of a material. =1 Conductivity is the reciprocal of resistivity. P = IV = I 2 R = V 2 R Computes the electric power delivery to a resistor.