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 3800-Ω 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× −5105.2 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 12-V 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 3.5-m length of copper wire 1.5 mm in diameter?

8. Can a 2.5-mm-diameter 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 3.0-V portable CD player that draws a maximum of

320 mA of current?

10. (a) Determine the resistance of, and current through, a 75-W lightbulb connected to its proper source

voltage of 120 V. (b) Repeat for a 440-W bulb.

11. How many kWh of energy does a 550-W toaster use in the morning if it is in operation for a total of

15 min? At a cost of ,kWhcents0.9 estimate how much this would add to your monthly electric

energy bill if you made toast four mornings per week.

12. How many 100-W lightbulbs, connected to 120 V in parallel, can be used without blowing a 15-A

fuse?

13. A power station delivers 620 kW of power at 12,000 V to a factory through wires with total

resistance .0.3 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 12-V battery, and (b) what is its resistance? Assume the manufacturer’s claim of

60% efficiency.

15. Four Ω-240 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 Ω-650 and a Ω-2200 resistor are connected in series with a 12-V battery. What is the voltage

across the Ω-2200 resistor?

17. Suppose that you have a ,-680 Ω a ,-940 Ω and a Ωk-20.1 resistor. What is (a) the maximum, and (b)

the minimum resistance you can obtain by combining these?

18. Three Ω-240 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 110-V 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 7.0-W Christmas tree lights are connected in series to each other and to a 110-V source. What

is the resistance of each bulb?

21. Determine (a) the equivalent resistance of the circuit shown in Fig. 19–39, and (b) the voltage across

each resistor.

Applying Kirchhoff’s Rules

22. Determine the magnitudes and directions of the currents through 1R and 2R 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 ,18 ,25 21 Ω=Ω= RR

and .353 Ω=R

24. Calculate the currents in each resistor below.

25. What would the current 1I be in the diagram below if the Ω-12 resistor is shorted out? Let

.0.1 Ω=r

Capacitance

26. The two plates of a capacitor hold C2500 µ+ and C2500 µ− 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 0.20-F capacitor is desired. What area must the plates have if they are to be separated by a 2.2-mm

air gap?

29. An electric field of mV1050.8 5× is desired between two parallel plates, each of area 2cm0.35

and separated by 2.45 mm of air. What charge must be on each plate?

30. How strong is the electric field between the plates of a F-80.0 µ air-gap capacitor if they are 2.0 mm

apart and each has a charge of C?72 µ

31. A F-50.2 µ capacitor is charged to 857 V and a F-80.6 µ 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?

33. The electric field between the plates of a paper-separated )75.3( =K capacitor is .mV1024.8 4×

The plates are 1.95 mm apart, and the charge on each plate is C.775.0 µ 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 9-in. pie pans 5 cm apart and connecting them to

the opposite terminals of a 9-V 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 4.7-µF capacitors are connected in parallel. What is the equivalent capacitance? (b) What is

their equivalent capacitance if connected in series?

38. A F-00.3 µ and a F-00.4 µ capacitor are connected in series, and this combination is connected in

parallel with a F-00.2 µ 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?

*40. In the diagram below, suppose F.0.16321 µ=== CCC If the charge on 2C is C,0.242 µ=Q

determine the charge on each of the other capacitors, the voltage across each capacitor, and the

voltage V across the entire combination.

41. A F-40.0 µ and a F-60.0 µ capacitor are connected in series to a 9.0-V 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 250-pF 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?