Hai by the Water 345

Chapter 3: Current and Resistance

Quick Quizzes - QUESTIONS

1. Consider positive and negative charges moving horizontally through the four regions in Figure 17.2. Rank the magnitudes of the currents in these four regions from lowest to highest. (Ia is the current in Figure 17.2a, Ib the current in Figure 17.2b, etc.) (a) Id , Ia , Ic , Ib (b) Ia , Ic , Ib , Id (c) Ic , Ia , Id , Ib (d) Id , Ib , Ic , Ia (e) Ia , Ib , Ic , Id (f) none of these

[pic]
Figure 17.2

2. Suppose a current-carrying wire has a cross-sectional area that gradually becomes smaller along the wire, so that the wire has the shape of a very long cone. How does the drift speed vary along the wire? (a) It slows down as the cross section becomes smaller. (b) It speeds up as the cross section becomes smaller. (c) It doesn’t change. (d) More information is needed.

3. In Figure 17.7b, does the resistance of the diode (a) increase or (b) decrease as the positive voltage ΔV increases?

[pic]
Figure 17.7 (a) The current–voltage curve for an ohmic material. The curve is linear, and the slope gives the resistance of the conductor. (b) A nonlinear current–voltage curve for a semiconducting diode. This device doesn’t obey Ohm’s law.

4. Suppose an electrical wire is replaced with one having every linear dimension doubled (i.e. the length and radius have twice their original values). Does the wire now have (a) more resistance than before, (b) less resistance, or (c) the same resistance?

5. A voltage ΔV is applied across the ends of a nichrome heater wire having a cross-sectional area A and length L. The same voltage is applied across the ends of a second heater wire having a cross-sectional area A and length 2L. Which wire gets hotter? (a) the shorter wire, (b) the longer wire, or (c) more information is needed.

6. Two resistors, A and B, are connected in a series circuit with a battery. The resistance of A is twice that of B. Which resistor dissipates more power? (a) resistor A (b) resistor B (c) More information is needed.

Quick Quizzes - ANSWER

1. (d). Negative charges moving in one direction are equivalent to positive charges moving in the opposite direction. Thus, [pic] are equivalent to the movement of 5, 3, 4, and 2 charges respectively, giving [pic].

2. (b). Under steady-state conditions, the current is the same in all parts of the wire. Thus, the drift velocity, given by [pic], is inversely proportional to the cross-sectional area.

3. (b). The slope of the line tangent to the curve at a point is the reciprocal of the resistance at that point. Note that as [pic] increases, the slope (and hence [pic]) increases. Thus, the resistance decreases.

4. (b). Consider the expression for resistance: [pic]. Doubling all linear dimensions increases the numerator of this expression by a factor of 2, but increases the denominator by a factor of 4. Thus, the net result is that the resistance will be reduced to one-half of its original value.

5. (a). The resistance of the shorter wire is half that of the longer wire. The power dissipated, [pic], (and hence the rate of heating) will be greater for the shorter wire. Consideration of the expression [pic] might initially lead one to think that the reverse would be true. However, one must realize that the currents will not be the same in the two wires.

6. (a). The power dissipated by a resistor may be expressed as [pic]where I is the current carried by the resistor of resistance R. Since resistors connected in series carry the same current, the resistor having the largest resistance will dissipate the most power.