Electricity Review

 

1.      Everyone has noticed from time to time that clothes fresh out of the dryer can often have a static charge.  Suppose a sock coming out of the dryer is positively charged.  (a) Explain what you think might cause the sock to become charged.  (b) Explain how an object becomes positively charged by referring to what happens with the protons and/or electrons in the sock.  (c) The sock may “stick” to another piece of clothing – why?

2.      Some electroscopes consist of two metal foil “leaves” that hang from a common point and are free to move at the other end (see Figure 16-10, p. 480).  Suppose a certain plastic CPVC pipe becomes negatively charged by rubbing it with a wool pad.  The electroscope is then touched by the pipe, causing the two leaves to spread apart and form an inverted “V”.  (a) Explain what causes the leaves to spread apart.  (b) It is then noted that if another negative charge is brought near, but doesn’t touch, the leaves will move even farther apart – why?

3.      The Van de Graaff generator produces around 100000 Volts and makes impressive sparks.  And yet, in spite of this, it is not particularly dangerous nor is there very much energy involved.  Explain how the generator can have such a huge voltage but such a small amount of energy.

4.      Explain the difference between conductors and insulators.

5.      Three light bulbs of different resistance are connected together with wires.  If it is desired that the three bulbs have the same current flowing through them should the connection be series or parallel?  If it is desire that the three bulbs have the same voltage across them should the connection be series or parallel?  Make a sketch of each type of connection.

6.      A light bulb is connected to a battery.  Describe the energy conversions that take place in such a circuit.

7.      While in operation the metal sphere on top of the Van de Graaff might have a charge q = -2.0 μC.  Of which is there more in the sphere – protons or electrons and by how many?

8.      Two pith balls each of mass 0.1 g are situated 3.0 cm apart.  The charge on one is -2.0 nC and the charge on the other is -3.0 nC.  (a) Determine the electric force acting on each ball and state the direction as either repulsion or attraction.  (b) Assuming no other forces act on the balls, determine the acceleration of each one.  (c) If you were to watch the two balls interacting would it be possible to tell which one had the greater amount of charge by the observed behavior?

9.      In a Helium nucleus there are two protons and two neutrons.  Determine the amount of electric force acting on one of the protons given the approximate diameter of the nucleus is 4 × 10-15 m (assume the protons are this far apart).

10.  In a certain classroom demo the Van de Graaff generator is used to produce a charge of -2.5 μC on one metal sphere and a charge of +1.5 μC on another.  The centers of the two spheres are separated by 2.50 m.  A pith ball of charge -3.0 nC is then placed near the spheres.  (a) If the pith ball is 0.50 m away from the center of the negative sphere and 2.0 m away from the center of the positive sphere what will be the net electric force including direction?  (b) If the ball is mass 0.1 g what will be its resulting acceleration (ignoring all other forces)?  (c) At what point along a line passing through the two spheres will the net electric force on the pith ball be zero.

11.  Suppose the positive sphere in the previous problem is removed but the negative sphere and pith ball remain.  If the pith ball is slowly lowered from directly above the sphere at what distance from the center would the electric force be great enough to make the pith ball “float”?  (i.e. at what point would the electric force equal the weight of the ball?)

12.  Three point charges are arranged in an equilateral triangle of side 10.0 cm.  The values of charge are:  q1 = -5.0 nC, q2 = +2.0 nC, q3 = +2.0 nC.  Determine the net electric force on the charge q1.

13.  A particular dry cell is rated at 1.5 volts.  How much electric potential energy does a single electron gain by passing through the cell?

14.  A pith ball of mass 0.10 g and charge 3.0 nC is observed to accelerate from 0 to 5.0 m/s as it moves a distance of 20 cm away from a charged sphere.  Estimate the electric potential difference between the beginning and end of this motion (ignore gravity).  Hint: the ball is gaining kinetic energy!

15.  The Van de Graaff generator moves about 2 μC of charge from one sphere to another in around 0.5 s.  (a) Determine the average current through the generator.  Note: this current exists in the form of “static” charge moving along on the rubber belt!  (b) If a spark jumps from one sphere to the other in 0.01 s, what is the current through the air?

16.  A 6.0 V battery is connected to a light bulb that draws 0.15 A current.  The bulb remains lit for 4.0 hours before the battery is completely drained.  (a) Determine the resistance of the bulb.  (b) Determine the power of the bulb.  (c) Determine the amount of chemical energy originally stored in the battery.  (d) Determine the total amount of charge that passes through the circuit during the 4.0 hour period.

17.  The resistance of a wire will increase as the wire heats up (for most types of wire).  (a) Based on this, when will the current through a light bulb be greatest – right after it is turned on or at some point after the bulb has been on for a while?  Explain your answer.  (Hint: the voltage applied to the bulb is relatively constant.)  (b) Is this consistent with the fact that a light bulb is likely to burn out at the instant it is turned on?  Explain.

18.  A 40 W light bulb in your house operates on 120 V.  Determine the resistance such a bulb.  Does a greater wattage bulb have a greater or lesser resistance than this?  Explain.

19.  If the positive and negative terminals of a battery are connected by a wire the wire will get very hot and the battery will rapidly lose its energy and “die”.  Explain in specific terms why this would happen, referring to electric potential, current, energy, power, resistance, etc.

20.  A particular flashlight consists of three D-cells, each 1.5 V, that are “stacked” in series and power a bulb of resistance 8.0 W.  (a) Determine the current and power for the bulb.   (b) Suppose the flashlight is redesigned so that the three cells are connected in parallel instead of series.  Determine the current and power for the bulb.  (c) Suppose that each cell is a rechargeable type with a rating of 1800 mA-h.  Determine the amount of time the bulb will stay lit for both the series case and the parallel case.

21.  Three resistors are connected to a 9.00 V battery:  R1 = 100 W, R2 = 200 W, R3 = 300 W.  Determine the voltage, current, and power for each resistor for (a) a series connection, and (b) a parallel connection.

22.  A bulb with a resistance of 240 W connected to 120 V has a power of 60.0 W.  Now suppose the same bulb is connected to 120 V using 300 feet of extension cords.  This may be viewed as a series connection in which current flows through 300 feet of wire to the bulb and then back through another 300 feet of wire.  Each 300 foot section of wire has resistance 2.0 W.  (a) Determine the effective resistance of the bulb and extension cord.  (b) Determine the current through the cord.  (c) Determine the voltage and power for the bulb in this situation.  (d) Determine the wattage of the extension cord.

23.  In typical household wiring each circuit breaker controls several outlets.  Everything plugged into these outlets is connected in parallel to 120 V and the circuit breaker limits the total current.  Suppose a 1200 W hair dryer, a 75 W bulb, an 1800 W heater and a 250 W television are all connected to the same circuit.  (a) Determine the current for each device and the total current through the breaker.  (b) Determine the effective resistance of the four devices connected in parallel.

 

Answers

 

1. 

2.

3.

4.

5.

6.

7. 12 trillion more electrons than protons

8.  a. 6.0 × 10-5 N repulsion

     b. each accelerates 0.60 m/s2 away

         from the other

     c. No – why not?

9.  14 N repulsion

10. a. 2.80 × 10-4 N toward pos. sphere
      b. 2.8 m/s2 toward pos. sphere

      c. 8.6 m from the pos. and 11.1 m

           from the neg.

11. 0.26 m above the center of the sphere

12. 16 μN toward the center of the

        triangle

13. 2.4 × 10-19 J

14. 420 kV

15. a. 4 μA

      b. 0.2 mA

16. a. 40 W

      b. 0.90 W
      c. 13 kJ

      d. 2200 C

17.

18. 360 W; less – why?

19.

20. a. 0.56 A, 2.5 W

      b. 0.19 A, 0.28 W

      c. series: 3.2 h; parallel: 29 h

21. a. I = 15.0 mA for all three

          V1 = 1.50 V; P1 = 22.5 mW

          V2 = 3.00 V; P2 = 45.0 mW

          V3 = 4.50 V; P3 = 67.5 mW

      b. V = 9.00 V for all three

          I1 = 90.0 mA; P1 = 810 mW

          I2 = 45.0 mA; P2 = 405 mW

          I3 = 30.0 mA; P3 = 270 mW

22. a. 244 W

      b. 0.492 A

      c. 118 V; 58.0 W

      d. 0.97 W

23. a. 10 A, 0.63 A, 15 A, 2.1 A; 28 A

      b. 4.3 W