DC Circuits. Circuits and Capacitance Worksheet. 10 Ω resistance. second? on the sodium is the same as on an electron, but positive.


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1 Circuits and Capacitance Worksheet DC Circuits 1. A current of 1.30 A flows in a wire. How many electrons are flowing past any point in the wire per second? 2. What is the current in amperes if 1200 Na + ions flow across a cell membrane in 3.5 µs? The charge on the sodium is the same as on an electron, but positive. 3. What voltage will produce 0.25 A of current through a 3800Ω resistor? 4. An electric clothes dryer has a heating element with a resistance of 9.6 Ω. (a) What is the current in the element when it is connected to 240 V? (b) How much charge passes through the element in 50 min? 5. A bird stands on a dc electric transmission line carrying 2800 A. The line has Ω resistance per meter, and the bird s feet are 4.0 cm apart. What is the potential difference between the bird s feet? 6. A 12V battery causes a current of 0.60 A through a resistor. (a) What is its resistance, and (b) how many joules of energy does the battery lose in a minute? 7. What is the resistance of a 3.5m length of copper wire 1.5 mm in diameter? 8. Can a 2.5mmdiameter copper wire have the same resistance as a tungsten wire of the same length? Give numerical details. 9. What is the maximum power consumption of a 3.0V portable CD player that draws a maximum of 320 ma of current? 10. (a) Determine the resistance of, and current through, a 75W lightbulb connected to its proper source voltage of 120 V. (b) Repeat for a 440W bulb. 11. How many kwh of energy does a 550W toaster use in the morning if it is in operation for a total of 15 min? At a cost of 9.0 cents kwh, estimate how much this would add to your monthly electric energy bill if you made toast four mornings per week. 12. How many 100W lightbulbs, connected to 120 V in parallel, can be used without blowing a 15A fuse? 5
2 13. A power station delivers 620 kw of power at 12,000 V to a factory through wires with total resistance 3.0 Ω. How much less power is wasted if the electricity is delivered at 50,000 V rather than 12,000 V? 14. A small immersion heater can be used in a car to heat a cup of water for coffee or tea. If the heater can heat 120 ml of water from 25 C to 95 C in 8.0 min, (a) approximately how much current does it draw from the car s 12V battery, and (b) what is its resistance? Assume the manufacturer s claim of 60% efficiency. 15. Four 240 Ω lightbulbs are connected in series. What is the total resistance of the circuit? What is their resistance if they are connected in parallel? 16. A 650 Ω and a Ω resistor are connected in series with a 12V battery. What is the voltage across the Ω resistor? 17. Suppose that you have a 680Ω, a 940Ω, and a 1.20kΩ resistor. What is (a) the maximum, and (b) the minimum resistance you can obtain by combining these? 18. Three 240 Ω resistors can be connected together in four different ways, making combinations of series and/or parallel circuits. What are these four ways, and what is the net resistance in each case? 19. Eight identical lights are connected in series across a 110V line. (a) What is the voltage across each bulb? (b) If the current is 0.50 A, what is the resistance of each bulb, and what is the power dissipated in each? 20. Eight 7.0W Christmas tree lights are connected in series to each other and to a 110V source. What is the resistance of each bulb? 21. Determine (a) the equivalent resistance of the circuit shown in Fig , and (b) the voltage across each resistor.
3 Applying Kirchhoff s Rules 22. Determine the magnitudes and directions of the currents through R 1 and R 2 in the diagram below 23. Determine the magnitudes and directions of the currents in each resistor shown below. The batteries have emfs of ε 1 = 9.0V and ε 2 = 12.0V and the resistors have values of R 1 = 25 Ω, R2 = 18 Ω, and R = Ω 24. Calculate the currents in each resistor below.
4 25. What would the current I 1 be in the diagram below if the 12 Ω resistor is shorted out? Let r = 1.0 Ω. Capacitance 26. The two plates of a capacitor hold µ C and 2500 µ C of charge, respectively, when the potential difference is 850 V. What is the capacitance? 27. The potential difference between two short sections of parallel wire in air is 120 V. They carry equal and opposite charge of magnitude 95 pc. What is the capacitance of the two wires? 28. A 0.20F capacitor is desired. What area must the plates have if they are to be separated by a 2.2mm air gap? An electric field of V m is desired between two parallel plates, each of area and separated by 2.45 mm of air. What charge must be on each plate? cm 30. How strong is the electric field between the plates of a 0.80µ F airgap capacitor if they are 2.0 mm apart and each has a charge of 72 µ C? 31. A 2.50µ F capacitor is charged to 857 V and a 6.80µ F capacitor is charged to 652 V. These capacitors are then disconnected from their batteries. Next the positive plates are connected to each other and the negative plates are connected to each other. What will be the potential difference across each and the charge on each? [Hint: charge is conserved.] 32. What is the capacitance of a pair of circular plates with a radius of 5.0 cm separated by 3.2 mm of mica?
5 33. The electric field between the plates of a paperseparated ( K = 3.75) capacitor is V m. The plates are 1.95 mm apart, and the charge on each plate is µ C. Determine the capacitance of this capacitor and the area of each plate. 34. A cardiac defibrillator is used to shock a heart that is beating erratically. A capacitor in this device is charged to 5.0 kv and stores 1200 J of energy. What is its capacitance? 35. A homemade capacitor is assembled by placing two 9in. pie pans 5 cm apart and connecting them to the opposite terminals of a 9V battery. Estimate (a) the capacitance, (b) the charge on each plate, (c) the electric field halfway between the plates, and (d) the work done by the battery to charge the plates. (e) Which of the above values change if a dielectric is inserted? 36. How does the energy stored in a capacitor change if (a) the potential difference is doubled, and (b) the charge on each plate is doubled, as the capacitor remains connected to a battery? 37. (a) Six 4.7µF capacitors are connected in parallel. What is the equivalent capacitance? (b) What is their equivalent capacitance if connected in series? 4 parallel with a 38. A 3.00µ F and a 4.00µ F capacitor are connected in series, and this combination is connected in 2.00µ F capacitor (see below). What is the net capacitance? 39. The capacitance of a portion of a circuit is to be reduced from 4800 pf to 2900 pf. What capacitance can be added to the circuit to produce this effect without removing existing circuit elements? Must any existing connections be broken in the process?
6 *40. In the diagram below, suppose C 1 = C2 = C3 = 16.0 µ F. If the charge on C 2 is Q 2 = 24.0 µ C, determine the charge on each of the other capacitors, the voltage across each capacitor, and the voltage V across the entire combination. 41. A 0.40µ F and a 0.60µ F capacitor are connected in series to a 9.0V battery. Calculate (a) the potential difference across each capacitor, and (b) the charge on each. (c) Repeat parts (a) and (b) assuming the two capacitors are in parallel. 42. A circuit contains a single 250pF capacitor hooked across a battery. It is desired to store three times as much energy in a combination of two capacitors by adding a single capacitor to this one. How would you hook it up, and what would its value be?
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