Unit 8 AP Practice Problems Current Electricity and RC Circuits

Unit 8 AP Practice Problems----Current Electricity and RC Circuits

1. *An automobile headlight with a resistance of 30  is placed across a 12V battery. What is the current through the circuit? (0.4 amp) 2. A motor with an operating resistance of 32  is connected to a voltage source. The current in the circuit is 3.8 A. What is the voltage of the source? (121.6 v) 3. A transistor radio uses 2 x 10-4 A of current when it is operated by a 3V battery. What is the resistance of the radio circuit? (1.5 E4 ohm) 4. *Draw a series circuit diagram showing a 4.5-V battery, a resistor, and an ammeter reading 90 mA. a. Label the size of the resistor. (50 ohm) b. Label the direction of “conventional current”. Is this the same as the direction of electron flow? c. Add a voltmeter that measures the potential difference across the resistor. 5. Draw a circuit diagram to include a 60-V battery, a resistor of 12.5  in series with an ammeter, and a voltmeter across the resistor. Indicate the ammeter reading and the direction of electron flow and conventional current. (4.8 A) 6. *How many electrons flow through a battery that delivers a current of 2.7 A for 25 s? (4.22 E20) 7. A 250 resistor is across a 120V outlet. What net charge passes through any point in the circuit during a 1minute interval? (28.8 C) 8. *A lamp draws a current of 0.5 A when it is connected to a 120-V source. a. What is the resistance of the lamp? (240 ohm) b. What is the power consumption of the lamp? (60 W) 9. A 75W lamp is connected to 120 V. a. How much current flows through the lamp? (0.625 A) b. What is the resistance of the lamp? (192 ohm) 10. A car battery causes a current of 2.0 A to flow through a lamp while 12 V is across it. What is the power rating of the lamp? (24 W) 11. The current through a light bulb connected across the terminals of a 120V outlet is 0.5A. At what rate does the bulb convert electric energy to light? (60 W) 12. The current through the starter motor of a car is 210 A. If the battery keeps 12 V across the motor, what electric energy is delivered to the starter in 10.0 s? (2.52 E4 J) 13. A 5A current is maintained in a simple circuit with a total resistance of 3 . How much energy is dissipated in 6 seconds? (450 J) 14. A 15 electric heater operates on a 120V outlet. a. What is the current through the heater? (8 A) b. How much energy is used by the heater in 30.0 s? (2.88 E 4 J) c. Assuming 100% efficiency, how much thermal energy is liberated by the heater in this time? (2.88 E 4 J) 15. A 30 resistor is connected across a 60-V battery. a. What is the current in the circuit? (2 A) b. How much energy is used by the resistor in 5 min? (3.60 E4 J) 16. *Determine the length of a copper wire that has a resistance of 0.23 anda cross-sectional area of 1.8 x 103 m2. The resistivity of copper is 1.72  108  • m. (2.41 E4 m) 17. The resistivity of a silver wire is 1.59  108  • m. The radius of the wire is 9.08  103 m. If the length of the wire is 2.00 m, what is the resistance of the wire? (1.23 E-4 ohm) 18. *A clock uses1.5 A of current when it is plugged into a 120 V outlet. It is never turned off. What is the yearly cost of operating the monitor if the cost of electricity is $0.12/kWh?

Series and Parallel Circuits (Draw each circuit prior to doing the math) 19. *There are three 20 resistors connected in series across a 120V generator. a. What is the effective (equivalent) resistance of the circuit? (60 ohm) b. What is the current in the circuit? (2 A) c. What is the voltage drop across each resistor? (40 v) d. What is the power of each resistor? (80 W) 20. A 10 resistor, a 15 resistor, and a 5 resistor are connected in series across a 90V battery. a. What is the equivalent resistance of the circuit? (30 ohm) b. What is the current in the circuit? (3 A) c. What is the voltage drop across each resistor? (30 v, 45 v, 15 v) d. What is the power of each resistor? (90 W, 135 W, 45 W)

Unit 8 AP Practice Problems Current Electricity and RC Circuits 1 21. Four resistors (12, 16, 22, and 27) are connected in series across a 60V battery. a. What is the equivalent resistance of the circuit? (77 ohm) b. What is the current in the circuit? (0.779 A) c. What is the voltage drop across each resistor? (9.35 v, 12.47 v, 17.14 v, 21.04 v) d. What is the power of each resistor? (7.28 W, 9.71 W, 13.35 W, 16.39 W) 22. A 9V battery is connected to three resistors in a series circuit. a. If you increase the resistance of one of the devices, how will the total circuit resistance change? (increase) b. What will happen to the current? (decrease) c. Will there be any change in the battery voltage? (nope….not controlled by I or R) 23. Ten identical bulbs are connected in series with each other. When connected to a 120V outlet, the current through the bulbs is 0.06 A. a. What is the equivalent resistance of the circuit? (2000 ohm) b. What is the resistance of each bulb? (200 ohm) c. What is the power of each bulb? (0.72 W) 24. *Three 15 resistors are connected in parallel with each other and placed across a 30V potential difference. a. What is the equivalent resistance of the parallel circuit? (5 ohm) b. What is the total current through the entire circuit? (6 A) c. What is the voltage drop across each branch in the circuit? (30 v) d. What is the current through each individual branch of the parallel circuit? (2 A) 25. A 12.0 resistor and a 15.0 resistor are connected in parallel and placed across the terminals of a 15.0V battery? a. What is the equivalent (total) resistance of the parallel circuit? (6.67 ohm) b. What is the total current through the entire circuit? (2.25 A) c. What is the voltage drop across each branch in the circuit? (15 v) d. What is the current through each individual branch of the parallel circuit? (1.25 A, 1 A) e. Suppose a 20 ohm resistor is added parallel to the initial two, does the equivalent resistance become smaller, larger, or remain the same? (smaller  5 ohm) f. What would happen to the total current? ( increase to 3 A) g. How would that effect the amount of current through the 15.0- resistor? (wouldn’t change as that resistor will draw its own current independent of the other two resistors) 26. A 120.0 resistor, a 60.0 resistor, and a 40.0 resistor are connected in parallel to each other and placed across a potential difference of 12.0 V. a. What is the equivalent resistance of the parallel circuit? (20 ohm) b. What is the current through the entire circuit? (0.6 A) c. What is the voltage drop across each branch in the circuit? (12 v) d. What is the current through each of the branches of the parallel circuit? (0.1 A, 0.2 A, 0.3 A) e. What is the power of each resistor? (1.2 W, 2.4 W, 3.6 W) Combination Circuits 1

60V 2 3 4 5 6

7 27. The above circuit has a 10 resistor at position 1 (R1), a 15 resistor at position 2 (R2), a 12 resistor at position 3 (R3), and a 17 resistor at position 7 (R7). Ignore all other branches for this particular problem. a. What is the total resistance of the circuit? (33.67 ohm) b. What is the total current of the circuit? (1.78 A) c. What is the voltage drop across R1? (17.82 v) d. What is the voltage drop across R7? (30.30 v) e. How much voltage does each of the two branches in the parallel portion of the circuit get? (11.87 v) f. What is the current through R2? (0.79 A) g. What is the current through R3? (0.99 A) h. What is the sum of I2 and I3? (1.78 A, the same as the total current) i. What is the power of the entire circuit? (106.8 W) j. What is the power of R1, R2, R3, and R7? (31.72 W, 9.38 W, 11.75 W, 53.93 W) k. What does the sum of all the answers in the previous part (j) equal? (total power  106.78 W) Unit 8 AP Practice Problems Current Electricity and RC Circuits 2 Capacitors in Series and Parallel 28. *A 4 uF and an 8 uF capacitor are connected in parallel across a 25 V battery. Find a. The equivalent capacitance. (1.2 E-5 F) b. The total charge on the two capacitors. (3 E-4 C) 29. *Three capacitors (3, 7, and 9 uF) are connected in series. What is their equivalent capacitance? (1.70 E-6 F) 30. *Determine the equivalent capacitance between A and B for the group of capacitors in the drawing below. (2.03 E-6 F) A 5 uF 24 uF 4 uF 12 uF

B 6 uF 8 uF

31. *Three capacitors (4, 6, 12 uF) are connected in series across a 50 V battery. Find the voltage across each capacitor. (25 v, 16.67 v, 8.33 v) 32. For the following RC circuit, what is the circuit current a. when it is initially connected? (2.47 A) b. after it has been connected for a long time? (1 A)

6 uF 12 V 10 Ω 4Ω

33. The circuit below shows two resistors, a capacitor, and a 12 V battery. a. When the capacitor is fully charged, what is the total current in the circuit? (2 A) b. At this time, what is the voltage drop across the 2 ohm resistor? (4 v) c. At this time, what is the voltage drop across the 4 ohm resistor? (8 v) d. At this time, what is the magnitude of charge on one of the plates of the capacitor? (7.2 E-5 C) e. What is the total energy stored in the capacitor? (2.88 E-4 J)

12 V 4Ω 9 uF

34. Answer the following questions for the circuit below

5 uF 12 V 6 Ω 7 uF

a. what is the total current when it is just hooked up? (4 A; the branch with the capacitors will cause a short circuit and bypass the 6 ohm resistor) Once the capacitors are fully charged, what is b. the total current? (1.33 A) c. the total capacitance? (2.92 E -6 F) d. the potential drop across the 3 ohm resistor? (3.99 v) e. the potential drop across the 6 ohm resistor and the branch with the capacitors? (8.01 v) f. the total charge stored by the capacitors? (2.34 E-5 C) g. the charge stored on each of the individual capacitors? (2.34 E -5 C for both as they are in series) Unit 8 AP Practice Problems Current Electricity and RC Circuits 3 h. the voltage drop across the 5 uF and the 7 uF capacitor when they are fully charged? (4.68 v, 3.34 v)

Unit 8 AP Practice Problems Current Electricity and RC Circuits 4