A switch has a variable resistance that is nearly zero when closed and extremely large when open, and it is placed in series with the device it controls. Explain the effect the switch in Figure 4.46 has on current when open and when closed.

Figure 4.46 A switch is ordinarily in series with a resistance and voltage source. Ideally, the switch has nearly zero resistance when closed but has an extremely large resistance when open. (Note that in this diagram, the script E represents the voltage [or electromotive force] of the battery.)

What is the voltage across the open switch in Figure 4.46?

There is a voltage across an open switch, such as in Figure 4.46. Why, then, is the power dissipated by the open switch small?

Why is the power dissipated by a closed switch, such as in Figure 4.46, small?

A student in a physics lab mistakenly wired a lightbulb, battery, and switch as shown in Figure 4.47. Explain why the bulb is on when the switch is open and off when the switch is closed. (Do not try this—it is hard on the battery!)

Figure 4.47 A wiring mistake put this switch in parallel with the device represented by $R\text{.}$ (Note that in this diagram, the script E represents the voltage [or electromotive force] of the battery.)

Knowing that the severity of a shock depends on the magnitude of the current through your body, would you prefer to be in series or parallel with a resistance, such as the heating element of a toaster, if shocked by it? Explain.

Would your headlights dim when you start your car’s engine if the wires in your automobile were superconductors? (Do not neglect the battery’s internal resistance.) Explain.

Some strings of holiday lights are wired in series to save wiring costs. An old version utilized bulbs that break the electrical connection, like an open switch, when they burn out. If one such bulb burns out, what happens to the others? If such a string operates on 120 V and has 40 identical bulbs, what is the normal operating voltage of each? Newer versions use bulbs that short circuit, like a closed switch, when they burn out. If one such bulb burns out, what happens to the others? If such a string operates on 120 V and has 39 remaining identical bulbs, what is then the operating voltage of each?

If two household lightbulbs rated 60 W and 100 W are connected in series to household power, which will be brighter? Explain.

Suppose you are doing a physics lab that asks you to put a resistor into a circuit, but all the resistors supplied have a larger resistance than the requested value. How would you connect the available resistances to attempt to get the smaller value asked for?

Before World War II, some radios got power through a resistance cord that had a significant resistance. Such a resistance cord reduces the voltage to a desired level for the radio’s tubes and the like, and it saves the expense of a transformer. Explain why resistance cords become warm and waste energy when the radio is on.

Some lightbulbs have three power settings (not including zero), obtained from multiple filaments that are individually switched and wired in parallel. What is the minimum number of filaments needed for three power settings?

Is every emf a potential difference? Is every potential difference an emf? Explain.

Explain which battery is doing the charging and which is being charged in Figure 4.48.

Given a battery, an assortment of resistors, and a variety of voltage and current measuring devices, describe how you would determine the internal resistance of the battery.

Two different 12-V automobile batteries on a store shelf are rated at 600 and 850 amps. Which has the smallest internal resistance?

What are the advantages and disadvantages of connecting batteries in series? In parallel?

Semitractor trucks use four large 12-V batteries. The starter system requires 24 V, while normal operation of the truck’s other electrical components utilizes 12 V. How could the four batteries be connected to produce 24 V? To produce 12 V? Why is 24 V better than 12 V for starting the truck’s engine (a very heavy load)?

Can all of the currents going into the junction in Figure 4.49 be positive? Explain.

Apply the junction rule to junction b in Figure 4.50. Is any new information gained by applying the junction rule at e? (In the figure, each emf is represented by script E.)

(a) What is the potential difference going from point a to point b in Figure 4.50? (b) What is the potential difference going from c to b? (c) From e to g? (d) From e to d?

Apply the loop rule to loop afedcba in Figure 4.50.

Apply the loop rule to loops abgefa and cbgedc in Figure 4.50.

Why should you not connect an ammeter directly across a voltage source as shown in Figure 4.51? (Note that script E in the figure stands for emf.)

Figure 4.51

Suppose you are using a multimeter (one designed to measure a range of voltages, currents, and resistances) to measure current in a circuit and you inadvertently leave it in a voltmeter mode. What effect will the meter have on the circuit? What would happen if you were measuring voltage but accidentally put the meter in the ammeter mode?

Specify the points to which you could connect a voltmeter to measure the following potential differences in Figure 4.52: (a) the potential difference of the voltage source; (b) the potential difference across $R_1\text{;}$ (c) across $R_2\text{;}$ (d) across $R_3\text{;}$ (e) across $R_2$ and $R_3\text{.}$ Note that there may be more than one answer to each part.

Figure 4.52

To measure currents in Figure 4.52, you would replace a wire between two points with an ammeter. Specify the points between which you would place an ammeter to measure the following: (a) the total current; (b) the current flowing through $R_1\text{;}$ (c) through $R_2\text{;}$ (d) through $R_3\text{.}$ Note that there may be more than one answer to each part.

Why can a null measurement be more accurate than one using standard voltmeters and ammeters? What factors limit the accuracy of null measurements?

If a potentiometer is used to measure cell emfs on the order of a few volts, why is it most accurate for the standard ${\text{emf}}_{\text{s}}$ to be the same order of magnitude and the resistances to be in the range of a few ohms?

Regarding the units involved in the relationship $\tau =\text{RC}\text{,}$ verify that the units of resistance times capacitance are time, that is, $\Omega \cdot \mathrm{F}=\mathrm{s}\text{.}$

The $\text{RC}$ time constant in heart defibrillation is crucial to limiting the time the current flows. If the capacitance in the defibrillation unit is fixed, how would you manipulate resistance in the circuit to adjust the $\text{RC}$ constant $\tau$? Would an adjustment of the applied voltage also be needed to ensure that the current delivered has an appropriate value?

When making an ECG measurement, it is important to measure voltage variations over small time intervals. The time is limited by the $\text{RC}$ constant of the circuit—it is not possible to measure time variations shorter than $\text{RC}\text{.}$ How would you manipulate $R$ and $C$ in the circuit to allow the necessary measurements?

Draw two graphs of charge versus time on a capacitor. Draw one for charging an initially uncharged capacitor in series with a resistor, as in the circuit in Figure 4.41, starting from $\text{t}=0\text{.}$ Draw the other for discharging a capacitor through a resistor, as in the circuit in Figure 4.42, starting at $\text{t}=0\text{,}$ with an initial charge $Q_0\text{.}$ Show at least two intervals of $\tau \text{.}$

When charging a capacitor, as discussed in conjunction with Figure 4.41, how long does it take for the voltage on the capacitor to reach emf? Is this a problem?

When discharging a capacitor, as discussed in conjunction with Figure 4.42, how long does it take for the voltage on the capacitor to reach zero? Is this a problem?

Referring to Figure 4.41, draw a graph of potential difference across the resistor versus time, showing at least two intervals of $\tau \text{.}$ Also draw a graph of current versus time for this situation.

A long, inexpensive extension cord is connected from inside the house to a refrigerator outside. The refrigerator doesn’t run as it should. What might be the problem?

In Figure 4.44, does the graph indicate the time constant is shorter for discharging than for charging? Would you expect ionized gas to have low resistance? How would you adjust $R$ to get a longer time between flashes? Would adjusting $R$ affect the discharge time?

An electronic apparatus may have large capacitors at high voltage in the power supply section, presenting a shock hazard even when the apparatus is switched o1ff. A bleeder resistor is therefore placed across such a capacitor, as shown schematically in Figure 4.53, to bleed the charge from it after the apparatus is off. Why must the bleeder resistance be much greater than the effective resistance of the rest of the circuit? How does this affect the time constant for discharging the capacitor?

Figure 4.53 A bleeder resistor $R_{\text{bl}}$ discharges the capacitor in this electronic device once it is switched off.