Electricity Review Problems
KEY
1. Two unequal resistors are wired in parallel to a battery. One resistor is very large, the other very small. What is the effect of breaking the circuit where the large resistor is: a. On the total current in the circuit? A small change in current – just that due to the current flowing through the large resistor. b. On the total voltage? No change to voltage. c. On the total resistance of the circuit? The total resistance will increase (by a small amount) to equal the resistance of the small resistor. d. Draw a circuit like this. Make up voltages and resistances and demonstrate your answers. 2. You have a complex circuit and you decide to add another resistor. a. Describe where you would add the resistor in order to reduce the overall resistance. In parallel with another resistor. b. Again, draw such a circuit and demonstrate your answer. c. Does the power increase or decrease when you do this? Power should increase because you are using more current (even though resistance decreases…the effect is less). 3. Fuses and circuit breakers protect circuits by breaking the flow of current when the current becomes too high. a. Does it make sense to wire the circuit breaker in parallel or series? Why? Series – you want the entire current flowing through the circuit breaker so it stops the flow when dangerous levels of current are flowing. 4. Draw a circuit with 2 identical resistors in parallel followed (in series with…) by 2 more identical resistors in parallel. What might be an advantage of using 2 identical resistors in parallel instead of using a single resistor? When one resistor fails, the other(s) would still be lit. Equal brightness of lights. Others? 5. A 4.0 Ω resistor, an 8.0 Ω resistor, and a 12 Ω resistor are connected in series with a 24 V battery. Determine: a. The equivalent resistance 24 ohms
b. The current in the circuit 1 A 6. A 4.0 Ω resistor, an 8.0 Ω resistor, and a 12 Ω resistor are connected in parallel with a 24 V battery. Determine: a. The equivalent resistance 2.18 ohms b. The current in the circuit 11 A 7. A 1.6-meter long wire has a total resistance of 4.0 ohms. If you cut it into 3 parts: 0.3 meters, 0.5 meters and 0.8 meters: a. What is the resistance of each part? 0.75, 1.25 and 2 ohms b. If you wired these resistive wires in parallel what would the equivalent resistance of the circuit? 0.38 ohms 8. You have three resistors that total 9 Ω wired in parallel. Assuming only whole number Ω resistor: a. If you want to minimize the resistance what size resistors would you choose? 7, 1, and 1 b. If you want to maximize the resistance what size resistors would you choose? 3, 3, and 3 9. Three identical light bulbs are wired into a 12-volt circuit. 2 of them are in series and the 3rd is in a path parallel to both of the other lights. a. Draw this configuration and label the 2 light bulbs as “A” and “B” and the third as “C”. b. Comment on the brightness of each light bulb. A and B are the same. Both are more dim than C c. What happens when you unscrew light bulb A in terms of whether the other bulbs are lit and if they are brighter or dimmer than before. B goes out. C stays the same. d. Answer the same question for unscrewing light bulb C. A and B stay on and there is no difference in brightness. 10. Draw a complex circuit that has an 18 Ω resistor, a 9.0 Ω resistor and a 6.0 Ω resistor in parallel followed by a 12 Ω resistor in series. They are all attached to a 30.0 V battery. a. Find the equivalent resistance of the circuit and the current through each of the 3 resistors in parallel. 15 ohms, 18 ohm – 1/3 A, 9 ohm – 2/3 A, 6 ohm – 1 A.
11. The stockroom has only 20 Ω resistors and 50 Ω resistors. a. You need a resistance of 45 Ω. How can you create a circuit with this resistance? (2) 50’s in parallel followed by a 20 in series. b. How can you create a 35 Ω resistance in a circuit? (2) 50’s in parallel in series with (2) 20 in parallel. 12. Two identically parallel-wired strings of 25 bulbs are connected to each other in series. If the equivalent resistance of the combination is 150 Ω resistance when connected to a 120 V battery, what is the resistance of each bulb? 1875 ohms 13. A resistor with unknown resistance is connected in parallel to a 12 Ω resistor and then to a 12-volt battery. If the total current is 3.0 A what is the resistance of the unknown resistor? 2.0 A 14. Two resistors, “A” and “B” are connected in series to a 6.0 V battery. A voltmeter connected across “A” measures 4.0 V. When the 2 resistors are wired in parallel across the 6.0-V battery, the current in “B” is found to be 2.0 A. Find the resistances of “A” and “B”. 6.0 ohms and 3.0 ohms 15. Draw a schematic of nine 100 Ω resistors arranged in a complex circuit such that the equivalent resistance is equal to 100 Ω. [All nine resistors must be used!] Three groups of 3 resistors in parallel. 16. Your toaster oven and coffee maker each dissipate 1200 W of power. Can you operate both of these appliances at the same time if the 120 V line is protected with a 15-amp circuit breaker? Total current = 20 A therefore circuit breaker will open. 17. An electric heater is rated at 1300 W, a toaster is rated at 1100 W and an electric grill is rated at 1500 W. The three appliances are connected to the same circuit with a voltage of 120 V. a. Find the current and resistance in each appliance. Heater – 11A, Toaster – 9.2 A, Grill 12 A. b. Is a 30.0 A circuit breaker sufficient to protect this circuit? Too much for circuit.