Problem 41
A 34 -gauge copper wire, with a constant potential difference of \(0.10 \mathrm{~V}\) applied across its \(1.0 \mathrm{~m}\) length at room temperature \(\left(20 .{ }^{\circ} \mathrm{C}\right),\) is cooled to liquid nitrogen temperature \(\left(77 \mathrm{~K}=-196^{\circ} \mathrm{C}\right)\) a) Determine the percentage change in the wire's resistance during the drop in temperature. b) Determine the percentage change in current flowing in the wire. c) Compare the drift speeds of the electrons at the two temperatures.
Problem 42
A resistor of unknown resistance and a \(35-\Omega\) resistor are connected across a \(120-\mathrm{V}\) emf device in such a way that an 11 -A current flows. What is the value of the unknown resistance?
Problem 43
A battery has a potential difference of \(14.50 \mathrm{~V}\) when it is not connected in a circuit. When a \(17.91-\Omega\) resistor is connected across the battery, the potential difference of the battery drops to \(12.68 \mathrm{~V}\). What is the internal resistance of the battery?
Problem 44
When a battery is connected to a \(100 .-\Omega\) resistor, the current is \(4.00 \mathrm{~A}\). When the same battery is connected to a \(400 .-\Omega\) resistor, the current is 1.01 A. Find the emf supplied by the battery and the internal resistance of the battery.
Problem 45
A light bulb is connected to a source of emf. There is a \(6.20 \mathrm{~V}\) drop across the light bulb, and a current of 4.1 A flowing through the light bulb. a) What is the resistance of the light bulb? b) A second light bulb, identical to the first, is connected in series with the first bulb. The potential drop across the bulbs is now \(6.29 \mathrm{~V},\) and the current through the bulbs is \(2.9 \mathrm{~A}\). Calculate the resistance of each light bulb. c) Why are your answers to parts (a) and (b) not the same?
Problem 52
When a \(40.0-V\) emf device is placed across two resistors in series, a current of \(10.0 \mathrm{~A}\) is flowing in each of the resistors. When the same emf device is placed across the same two resistors in parallel, the current through the emf device is \(50.0 \mathrm{~A}\). What is the magnitude of the larger of the two resistances?
Problem 53
A voltage spike causes the line voltage in a home to jump rapidly from \(110 . \mathrm{V}\) to \(150 . \mathrm{V}\). What is the percentage increase in the power output of a 100.-W tungsten-filament incandescent light bulb during this spike, assuming that the bulb's resistance remains constant?
Problem 54
A thundercloud similar to the one described in Example 24.3 produces a lightning bolt that strikes a radio tower. If the lightning bolt transfers \(5.00 \mathrm{C}\) of charge in about \(0.100 \mathrm{~ms}\) and the potential remains constant at \(70.0 \mathrm{MV}\), find (a) the average current, (b) the average power, (c) the total energy, and (d) the effective resistance of the air during the lightning strike.
Problem 55
A hair dryer consumes \(1600 .\) W of power and operates at \(110 .\) V. (Assume that the current is \(D C .\) In fact, these are root-mean-square values of AC quantities, but the calculation is not affected. Chapter 30 covers AC circuits in detail.) a) Will the hair dryer trip a circuit breaker designed to interrupt the circuit if the current exceeds \(15.0 \mathrm{~A} ?\) b) What is the resistance of the hair dryer when it is operating?
Problem 56
How much money will a homeowner owe an electric company if he turns on a 100.00 -W incandescent light bulb and leaves it on for an entire year? (Assume that the cost of electricity is \(\$ 0.12 / \mathrm{kW} \mathrm{h}\) and that the light bulb lasts that long.) The same amount of light can be provided by a 26.000-W compact fluorescent light bulb. What would it cost the homeowner to leave one of those on for a year?
