Suppose a time machine has just brought you forward from 1750 (post-Newton but pre-electricity) and you’ve been shown the lightbulb demonstration of FIGURE Q27.1. Do observations or simple measurements you might make—measurements that must make sense to you with your 1700s knowledge—prove that something is flowing through the wires? Or might you advance an alternative hypothesis for why the bulb is glowing? If your answer to the first question is yes, state what observations and/or measurements are relevant and the reasoning from which you can infer that something must be flowing. If not, can you offer an alternative hypothesis about why the bulb glows that could be tested?

FIGURE Q27.1

Consider a lightbulb circuit such as the one in Figure Q27.1.

1. From the simple observations and measurements you can make on this circuit, can you distinguish a current composed of positive charge carriers from a current composed of negative charge carriers? If so, describe how you can tell which it is. If not, why not?

2. One model of current is the motion of discrete charged particles. Another model is that current is the flow of a continuous charged fluid. Do simple observations and measurements on this circuit provide evidence in favor of either one of these models? If so, describe how. If not, why not?

The electron drift speed in a wire is exceedingly slow—typically only a fraction of a millimeter per second. Yet when you turn on a flashlight switch, the light comes on almost instantly. Resolve this apparent paradox.

Is FIGURE Q27.4 a possible surface charge distribution for a current-carrying wire? If so, in which direction is the current? If not, why not?

FIGURE Q27.4

What is the difference between current and current density?

All the wires in FIGURE Q27.6 are made of the same material and have the same diameter. Rank in order, from largest to smallest, the currents $I_1$ to $I_4$. Explain.

FIGURE Q27.6

Both batteries in FIGURE Q27.7 are ideal and identical, and all lightbulbs are the same. Rank in order, from brightest to least bright, the brightness of bulbs A to C. Explain.

FIGURE Q27.7

Both batteries in FIGURE Q27.8 are ideal and identical, and all lightbulbs are the same. Rank in order, from brightest to least bright, the brightness of bulbs A to C. Explain.

FIGURE Q27.8

The wire in FIGURE Q27.9 consists of two segments of different diameters but made from the same metal. The current in segment 1 is $I_1$.

FIGURE Q27.9

1. Compare the currents in the two segments. That is, is $I_2$ greater than, less than, or equal to $I_1\text{?}$ Explain.

2. Compare the current densities $J_1$ and $J_2$ in the two segments.

3. Compare the electric field strengths $E_1$ and $E_2$ in the two segments.

4. Compare the drift speeds $(v_{\text{d}}){}_1$ and $(v_{\text{d}}){}_2$ in the two segments.

The current in a wire is doubled. What happens to (a) the current density, (b) the conduction-electron density, (c) the mean time between collisions, and (d) the electron drift speed? Are each of these doubled, halved, or unchanged? Explain.

The wires in FIGURE Q27.11 are all made of the same material. Rank in order, from largest to smallest, the resistances $R_{\text{A}}$ to $R_{\text{E}}$ of these wires. Explain.

FIGURE Q27.11

Which, if any, of these statements are true? (More than one may be true.) Explain. Assume the batteries are ideal.

1. A battery supplies the energy to a circuit.

2. A battery is a source of potential difference; the potential difference between the terminals of the battery is always the same.

3. A battery is a source of current; the current leaving the battery is always the same.