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AP Physics Quick Review – Electricity 1. Electrostatics Formulas F = kq1q2/r2 Like charges repel and unlike charges attract. The total charge of a system will be conserved. When charged objects of identical shapes and sizes are placed into contact, the objects will average out the total charge so each ends up with the same charge. The force between two charges is directly related to the product of the quantity of charge on each object and just like the gravitational force, the force follows the inverse square law with the distance. Practice Questions 1. Sphere A is neutral and it touches an identical sphere B that has an excess of 100 electrons. Then sphere A touches another identical sphere C that has an excess of 200 protons. What is the charges of spheres A , B and C? Sphere A Sphere B Sphere C A. +100 e + 100 e + 100 e B. -100 e -50 e +100 e C. -75 e -100 e -75 e D. +75 e -50 e +75 e 2. Two isolated charges, + q and - 2q, are 2 centimeters apart. If F is the magnitude of the force acting on charge -2q, what are the magnitude force acting on charge + q when they are 4 cm apart? A. F B. F/2 C. F/4 D. 2F 3. The diagram on the right shows 3 neutral metal spheres on insulating stands touching each other. A negative rod is brought near sphere X as shown in the diagram. The spheres are then separated and then the negative rod is removed. What will be the charges on the spheres? A. All three spheres will be positive. B. Sphere X will be positive, Y will be neutral and Z will be negative. C. Sphere X will be negative, Y will be neutral and Z will be positive. D. Sphere X will be negative, sphere Y will be positive and Z will be neutral. 4. A positively charged conductor attracts a second object. Which of the following statements could be true? Select two answers A. The second object is a conductor with positive net charge. B. The second object is a conductor with zero net charge. C. The second object is an insulator with zero net charge. D. The second object is an insulator with positive net charge. 5. Two negatively charged objects are held together by a 0.020 m length of insulating string as shown in the diagram above. The objects are initially at rest on a horizontal, non-conducting frictionless surface. The effect of gravity on each object due to the other is negligible. The charge of m1 is -4 nC and the charge of m2 is a -6 nC. a. Calculate the tension in the string. b. The string is now cut. On the axes below, qualitatively sketch a graph of the acceleration a of the object of mass m2 versus the distance d between the objects after the string has been cut. c. Describe qualitatively what happens to the speeds of the objects as time increases, assuming that the objects remain on the horizontal, non-conducting frictionless surface. 2. Current Electricity Formulas to know The resistance in a wire depends on the type of material at a specific temperature which relates to its resistivity (ρ) value, the length of wire (L) and the cross-sectional area of the wire (A). The cross-sectional area of a wire is equivalent to r2. If the diameter of a wire doubles, its cross-sectional area is quadrupled and that will lower its resistance to ¼ of its value. I = q/t R = ρL/A I = V/R P = VI Shorter, fatter, colder wires will have less resistance and be better choices for extension cords than long thin wires. Temperature will be directly related to resistance so as wires get hotter they have more resistance. Series: Resistance will remain constant if the material follows Ohm’s Law. Such materials are called “ohmic”. Rtotal= R1+R2+… Parallel 1/Rtotal= 1/R1+1/R2+… Ammeters measure current in amps. They are placed into a circuit and have very low resistances. Voltmeters measure potential difference (voltage) in volts and are placed around a resistor. They have very high resistance. Name Potential difference Resistance Current Power Energy Charge Variable V R I P W q unit Volt (V) Ohm ( Ampere (A) Watt (W) Joule (J) Coulomb (C) Practice Questions 1. If the 2 ohm resistor is replaced with another one with a smaller resistance value, then the A. ammeter reading will decrease and voltmeter reading will increase. B. ammeter reading will stay the same and the voltmeter reading will increase. C. ammeter and voltmeter readings will both increase. D. ammeter reading will increase and the voltmeter reading will stay the same. 2. The diagram below represents a lamp, a 10-volt battery, and a length of nichrome wire connected in series. Which of the following would increase the brightness of the lamp? 1. 2. 3. 4. Decrease the radius of the nichrome wire. Decrease the temperature of the room Increase the length of the nichrome wire. Put an ammeter into the circuit. 3. An air conditioner is designed to operate at 110 volts and is rated at 1800 watts. Is it possible to use the air conditioner in a circuit supplied with 110 volts, but which can carry a maximum current of 15 amperes before the circuit breaker is set off? [a] Yes, because the current needed is less than 15 amperes. [b] No, because the voltage required is too high. [c] Yes, because the voltage is lower than that needed. [d] No, because the current needed is greater than the 15 amperes 4. A student constructs the graph from data she collected on the current and voltage supplied to a lightbulb. Discuss whether the bulb is ohmic or not citing evidence from the graph. Series Circuit: Current is the same for all resistors and the total current is determined by the total resistance in the circuit. Resistors add together to get the total resistance. Voltage is shared among all of the resistors with more voltage going to larger resistors. A break anywhere in this circuit stops the current flowing in the circuit. Adding resistors in series increases the total resistance in the circuit. This will reduce to the total current to all the resistors and each resistor will get less voltage than before. Less power is usually generated in series circuits. Larger resistors will get more power than smaller resistors in this type of circuit. Be aware that lower wattage light bulbs have more resistance so lower wattage bulbs will be brighter than higher wattage bulbs in a series circuit. Parallel Circuit: Voltage is the same for all resistors. Each branch gets its own current and the total current is the sum of all of these individual currents. The branch with the lowest resistance gets the most current. Adding resistors in parallel reduces the total resistance in the circuit and will increase the total current, but the individual currents will not change. The equivalent resistance of a parallel circuit will always be less than the value of the smallest resistor in the circuit. More power is usually generated in parallel circuits. Smaller resistors get more power than larger resistors in this type of circuit so higher wattage bulbs will be brighter than lower wattage bulbs in a parallel circuit. The order of the components in the circuit does not matter as long as they are connected in series or parallel. Series-parallel combo: Determine which parts of the circuit are in parallel and which are in series and apply the appropriate rules stated above to each part. Redrawing the circuit and simplifying it can be helpful. Remember that the brightness of a bulb is determined by its power which is a product of its current and voltage. A bulb that is burned out will not get current flowing through it, but it may still have a potential difference across it. Practice Questions 1. A radio is designed to be operated with a voltage of 6 volts and needs 10 mA of current to operate properly. How will the radio be attached in a circuit with the 9 volt battery to function properly? A. The radio will be placed a series with a resistor of 300 ohms. B. The radio will be placed in parallel a resistor of 300 ohms. C. The radio will be placed in series with a 150 ohm resistor. D. The radio will be placed in parallel with a 150 ohm resistor. 2. The diagram below shows a circuit with two resistors. If another resistor is added in series to this circuit, what will happen to the ammeter reading? A. The ammeter reading will be greater. B. The ammeter reading will be lower. C. The ammeter reading will stay the same. D. It cannot be determined unless the value of the resistor is given. 3. The diagram represents an electric circuit consisting of four resistors and a 12-volt battery. If the 12 ohm resistor is removed, what happens to the ammeter and voltmeter readings? A. Ammeter and voltmeter increase. B. Ammeter and voltmeter decrease. C. Ammeter and voltmeter stay the same. D. Ammeter increases and voltmeter stays the same. 4. Two lamps are connected as shown. If lamp 1 burns out, then which of the following is true? A. The second lamp will go out also. B. The second lamp will stay lit, but will get dimmer. C. The second lamp will stay lit, but will get brighter. D. The second lamp will remain lit with the same brightness as before. 5. The circuit in the figure at the right contains two identical lightbulbs in series with a battery. At first both bulbs glow with equal brightness. When switch S is closed, which of the following occurs to the bulbs? Bulb I A. Goes out B. Gets brighter C. Gets brighter D. Gets slightly dimmer Bulb 2 Gets brighter Goes out Gets slightly dimmer Gets brighter V The series-parallel combination circuit at the left shows that resistors 1 and 2 are in series with a parallel combination of resistors 3 and 4. In this circuit, the ammeter is placed to read the total current which is the same current that resistors 1 and 2 get. The current through resistors 3 and 4 will be less than the total current but both currents will add to the total current in the circuit. The resistor with the lower resistance will get the greater current in the parallel section containing resistors 3 and 4. Resistors 3 and 4 get the same voltage as measured by the voltmeter, but it will not be the total voltage. The total voltage will be the sum of the voltages from the parallel combination (the voltmeter reading) and the voltages of resistors 1 and 2. Current is never used up in a circuit. The same current that leaves the battery must return to the battery. (Current follows the junction rule.) Voltage is used up by each resistor or parallel section so that the total volts left must be zero by the time the current returns to the battery.(This is the loop rule.) 2. If the current in the 3 ohm resistor is 0.5 A, what is the emf (voltage) of the power source? A. B. C. D. 1.5 V 3.0 V 4.5 V 6V 3. Five identical light bulbs -- A, B, C, D and E—are attached as shown. Assume the bulbs are ohmic and there is negligible resistance in the wires. If bulb D blows out, rank the bulbs from dimmest to brightest, placing equal brightness on the same line. Explain your ranking. Dimmest _____ _____ _____ _____ _____ Brightest