Honors Assignment – Electric Current and Circuits
Reading Chapter Sections: 18: 1 – 10; 19: 1 – 11
Objectives/HW
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The student will be able to: |
HW: |
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1 |
Define electric current and the Ampere and solve problems relating current to charge and time. |
1 – 3 |
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2 |
Solve problems involving electric power. |
4 – 10 |
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3 |
Define resistance the Ohm and solve problems using Ohm’s Law to relate voltage, current, and resistance. |
11 – 23 |
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4 |
Calculate the effective total resistance for multiple resistors connected in series or parallel and analyze DC circuits consisting of a combination of series and parallel branches of resistors and/or voltage sources, determining voltage and current for each element. |
24 – 37 |
Homework Problems
1. Just as a switch is turned on, a 10.0 amp fuse in an overloaded circuit melts and breaks in 0.15 s. Determine the minimum amount of charge that must have passed through the fuse in this time interval in order to cause it to “blow”.
2. How many electrons flow past a point in a wire each second if the wire has a current of 1.00 Amperes?
3. A certain rechargeable battery is rated at 400 mA×h. This is indicative of the total amount of electric charge it can deliver before it “dies”. (a) Determine this amount of charge. (b) If the battery is recharged in a time period of 5.0 h what is the required charging current?
4. The current through a toaster connected to a 120 V source is 8.0 A. What power is dissipated by the toaster?
5. A current of 1.2 A flows through a light bulb when it is connected across a 120 V source. What power is dissipated by the bulb?
6. A lamp draws 0.50 A from a 120 V generator. (a) How much power does the generator deliver to the lamp? (b) How much electric energy does the lamp convert to light and heat in a period of 5.0 minutes?
7. A 12 V automobile battery is connected to an electric starter motor. The current through the motor is 210 A. It takes 1.5 seconds to start the car’s engine. (a) What is the power used by the starter motor? (b) How much energy is used to start the car? (c) How much charge must pass through the starter motor (and through the battery) in order to start the car?
8. A 4.0 kW clothes dryer is connected to a 220 V circuit. How much current does the dryer use?
9. A flashlight bulb is connected across a 3.0 V power source. The current through the lamp is 1.5 A. (a) What is the power rating of the lamp? (b) How much electric energy does the lamp use in 11 minutes of operation?
10. A 60 W light bulb is connected to a voltage of 120 V and left on for 3.5 hours. The light bulb is 12% efficient. (a) How much electric charge passes through the bulb in this time period? (b) How much light energy is given off by the bulb in this time period? (c) How much heat energy is given off by the bulb in this time period?
11. A resistance of 60 W has a current of 0.40 A through it when it is connected to the terminals of a battery. What is the voltage of the battery?
12. What voltage must be applied to a 4.0 W resistor if the current is to be 1.5 A?
13. What voltage is placed across a motor of 15 W operating resistance if the current through it is 8.0 A?
14. A 75 V battery is connected to a 15 W resistor. (a) What is the current through the resistor? (b) What is the power output of the battery?
15. A 100 Watt light bulb operates on 120 Volts. Determine the resistance of the bulb.
16. A 12 V battery is connected to a certain device and it is observed that 24 mA current is drawn from the battery. (a) Determine the resistance of the device. (b) If the same device is connected to a 6.0 V battery how much current will be drawn?
17. The damage caused by electric shock depends on the current flowing through the body – 1 mA can be felt; 5 mA is painful. Above 15 mA, a person loses muscle control, and 70 mA can be fatal. A person with dry skin has a resistance from one arm to the other of about 100 kW. When skin is wet, the resistance drops to about 5 kW. (a) What is the minimum voltage placed across the arms that would produce a current that could be felt by a person with dry skin? (b) What current and what effect would the same voltage have if the person had wet skin? (c) What would be the minimum voltage that would produce a current that could be felt when the skin is wet?
18. A certain lamp draws 66 mA when connected to a 6.0 V battery and 75 mA when connected to a 9.0 V battery. (a) Show numerically whether or not this is an ohmic device (i.e. show whether or not the resistance is constant). (b) From 6.0 V to 9.0 V is a 50% increase in voltage. Determine the percent increase in power output of the lamp.
19. (a) Draw a schematic diagram to show a circuit that includes a 90 V battery, an ammeter, and a resistance of 45 W connected in series. Draw arrows showing the direction of conventional current flow and label the positive and negative terminals of the battery. (b) Determine the reading of the ammeter.
20. (a) Draw a series circuit diagram to include a 16 W resistor, a battery, and an ammeter that reads 1.75 A. Draw arrow showing the direction of conventional current flow and label the positive and negative terminals of the battery. (b) Determine the voltage of the battery.
21. A 220 W resistor is rated 5.0 W. This is the
maximum allowable power for the resistor.
(a) Determine the maximum allowable current that can flow through this
resistor.
(b) Determine the maximum allowable voltage to which this resistor should be
connected.
22. A certain wire in a household circuit has a resistance of 0.15 W and is designed to carry up to 15 A of current. (a) At its maximum current, what power is dissipated by the wire’s resistance? (b) How much heat does the wire give off in 10.0 minutes at its maximum capacity? (c) What is the electric potential difference from one end of the wire to the other when operated at its maximum capacity? (This is how much the voltage “drops” from its original value due to resistance of the wire.)
23. A transistor radio
operates by means of a 9.0 V battery that supplies it with a 50 mA
current. The cost of the battery is $0.90 and it will run the radio for 300
hours before going dead.
(a) What is the cost per kW-hr to operate the radio using the battery? (1
kW-hr is equal to 3.6 MJ) (b) The same radio, by means of a converter, is
plugged into a household circuit by a homeowner who pays $0.080 per kW-hr.
What does it now cost to operate the radio for 300 hours?
24. Why does the equivalent resistance decrease as more resistors are added to a parallel circuit?
25. Give at least two reasons why household wiring is done in parallel instead of in series.
26. (a) Why should an ammeter have a very low resistance? (b) Why should a voltmeter have a very high resistance?
27. Suppose you have two “D” cells and wish to use them to power a light bulb. The two batteries can either be connected in series or in parallel. (a) In order to achieve maximum voltage, how should the cells be connected? Explain. (b) In order to achieve maximum power, how should the cells be connected? Explain. (c) In order to last longest before going dead, how should the cells be connected? Explain. (d) How many times longer will the cells last when connected this way versus the other? Explain.
28. For each part of this
question, write the form of circuit that applies: series or parallel.
(a) The current is the same for each element in the circuit. (b) The voltage
is the same for each element in the circuit. (c) The total resistance is equal
to the sum of the individual resistances. (d) Adding a resistor decreases the
total resistance.
29. A 20.0 W lamp and a 5.00 W lamp are connected in series and placed
across a potential difference of 50.0 V. (a) Determine the equivalent
resistance of the two lamps.
(b) Determine the current delivered by the power source. (c) Determine the
voltage across each lamp. (d) Determine the power output of each lamp.
30. Three identical lamps are connected in series to a 6.0 V battery. What is the voltage drop across each lamp?
31. The load across a 12 V
battery consists of a series combination of three resistors of 15 W,
21 W, and 24 W. Determine the current in the circuit.
32. A current of 0.10 A flows in a series circuit consisting of a battery and two resistors: 15 W and 45 W. Determine the electric potential of the battery.
33. An electric potential of 5.0 V is required to run certain computer chips. A 6.0 V battery may be used to do this but it must be connect to two resistors in series. Supposing one has a resistance of 330 W what should the other be? (The computer chip will be driven by the voltage across only one of the two resistors.)
34. Three identical lamps are connected in parallel to each other and then connected to a 6.0 V battery. What is the voltage drop across each lamp?
35. A 40.0 V power source, a resistor of 16.0 W, and a resistor of 20.0 W are all connected in a parallel circuit. (a) Determine the equivalent resistance of the two resistors. (b) Determine the current supplied by the power source. (c) Determine the power dissipated by each resistor.
36. Consider the circuit
shown below. (a) Determine the current reading of the ammeter.
(b) Determine the voltage reading of the voltmeter. (c) Determine the power
dissipated by the 500 W
resistor.
37. Consider the circuit
shown below. (a) Determine the current reading of the ammeter.
(b) Determine the voltage reading of the voltmeter. (c) Determine the power
dissipated by the 45.0 W resistor.
Selected Answers