Homework Problems 2

1	(a) Many battery-operated devices take more than one battery. If you look closely in the battery compartment, you will see that the batteries are wired in series. Consider a flashlight circuit. What does the loop rule tell you about the effect of putting several batteries in series in this way? (b) The cells of an electric eel's nervous system are not that different from ours - each cell can develop a voltage difference across it of somewhere on the order of one volt. How, then, do you think an electric eel can create voltages of thousands of volts between different parts of its body?
2	The heating element of an electric stove is connected in series with a switch that opens and closes many times per second. When you turn the knob up for more power, the fraction of the time that the switch is closed increases. Suppose someone suggests a simpler alternative for controlling the power by putting the heating element in series with a variable resistor controlled by the knob. (With the knob turned all the way clockwise, the variable resistor's resistance is nearly zero, and when it's all the way counterclockwise, its resistance is essentially infinite.) (a) Draw schematics. (b) Why would the simpler design be undesirable?
3	A one-ohm toaster and a two-ohm lamp are connected in parallel with the 110-V supply of your house. (Ignore the fact that the voltage is AC rather than DC.) (a) Draw a schematic of the circuit. (b? ). For each of the three components in the circuit, find the current passing through it and the voltage drop across it. (c? ) Suppose they were instead hooked up in series. Draw a schematic and calculate the same things.	√
4	Wire is sold in a series of standard diameters, called "gauges." The difference in diameter between one gauge and the next in the series is about 20%. How would the resistance of a given length of wire compare with the resistance of the same length of wire in the next gauge in the series?
5	The figure shows two possible ways of wiring a flashlight with a switch. Both will serve to turn the bulb on and off, although the switch functions in the opposite sense. Why is the method shown in (a) preferable?
6	In the figure, the battery is 9 V. (a) What are the voltage differences across each light bulb? (b) What current flows through each of the three components of the circuit? (c) If a new wire is added to connect points A and B, how will the appearances of the bulbs change? What will be the new voltages and currents? (d) Suppose no wire is connected from A to B, but the two bulbs are switched. How will the results compare with the results from the original setup as drawn?
7	You have a circuit consisting of two unknown resistors in series, and a second circuit consisting of two unknown resistors in parallel. (a) What, if anything, would you learn about the resistors in the series circuit by finding that the currents through them were equal? (b) What if you found out the voltage differences across the resistors in the series circuit were equal? (c) What would you learn about the resistors in the parallel circuit from knowing that the currents were equal? (d) What if the voltages in the parallel circuit were equal?
8	A student in a biology lab is given the following instructions: "Connect the cerebral eraser (C.E.) and the neural depolarizer (N.D.) in parallel with the power supply (P.S.). (Under no circumstances should you ever allow the cerebral eraser to come within 20 cm of your head.) Connect a voltmeter to measure the voltage across the cerebral eraser, and also insert an ammeter in the circuit so that you can make sure you don't put more than 100 mA through the neural depolarizer." The diagrams show two lab groups' attempts to follow the instructions. (a) Translate diagram (a) into a standard-style schematic. What is correct and incorrect about this Problem 8. group's setup? (b) Do the same for diagram (b).
9	How many different resistance values can be created by combining three unequal resistors? (Don't count possibilities where not all the resistors are used.)
10	A person in a rural area who has no electricity runs an extremely long extension cord to a friend's house down the road so she can run an electric light. The cord is so long that its resistance, x, is not negligible. Show that the lamp's brightness is greatest if its resistance, y, is equal to x. Explain physically why the lamp is dim for values of y that are too small or too large.	∫
11	What resistance values can be created by combining a 1 kΩ resistor and a 10 kΩ resistor?
12	Suppose six identical resistors, each with resistance R, are connected so that they form the edges of a tetrahedron (a pyramid with three sides in addition to the base, i.e. one less side than an Egyptian pyramid). What resistance value or values can be obtained by making connections onto any two points on this arrangement?	S *
13	The figure shows a circuit containing five lightbulbs connected to a battery. Suppose you're going to connect one probe of a voltmeter to the circuit at the point marked with a dot. How many unique, nonzero voltage differences could you measure by connecting the other probe to other wires in the circuit?
14	The lightbulbs in the figure above (problem 13)are all identical. If you were inserting an ammeter at various places in the circuit, how many unique currents could you measure? If you know that the current measurement will give the same number in more than one place, only count that as one unique current.
15	The bulbs are all identical. Which one doesn't light up?	*
16	Each bulb has a resistance of one ohm. How much power is drawn from the one-volt battery?	*
17	The bulbs all have unequal resistances. Given the three currents shown in the figure, find the currents through bulbs A, B, C, and Ds.