PHYS 2212 Module 5 Self Assessment Practice Problems

Module 5 Self Assessment Practice Problems

5.1
Copper has 8.5 × 10²⁸ free electrons per cubic meter. A 73.0 cm length of 12-gauge copper wire, 2.05 mm in diameter, carries a current of 4.60 A. (Wire gauge describes a wire’s thickness — a smaller gauge number means a thicker wire.)
(a) How much time does it take for an electron to travel the length of the wire?
(b) Repeat part (a) for 6-gauge copper wire (diameter 4.12 mm) of the same length, carrying the same current.
(c) Generally speaking, how does changing the diameter of a wire carrying a given current affect the drift velocity of the electrons in the wire?
Answer: (a) 119 minutes (b) 480 minutes

5.2
In an ionic solution, a current consists of Ca²⁺ ions (charge +2e) and Cl⁻ ions (charge −e) traveling in opposite directions between two points, A and B.
(a) Every 0.580 min, 5.08 × 10¹⁸ Cl⁻ ions travel from A to B, while 3.20 × 10¹⁸ Ca²⁺ ions travel from B to A. What is the current (in mA) through this solution?
(b) In which direction (from A to B or from B to A) is the current in part (a) going? Explain.
Answer: (a) 53 mA (b) B to A

5.3
Nerve cells transmit electrical signals through their long, tubular axons. These signals propagate due to a sudden rush of Na⁺ ions, each with charge +e, into the axon. Measurements show that about 5.6 × 10¹¹ Na⁺ ions typically enter each meter of the axon over a time of 10 ms. What is the current associated with this inflow of charge?
Answer: 9 µA

5.4
A cylindrical rod, 1.50 m long with a diameter of 0.500 cm, is connected to a power supply that maintains a constant potential difference of 15.0 V across its ends. An ammeter measures the current through the rod. At room temperature (20.0°C), the ammeter reads 18.5 A. At 92.0°C, it reads 17.2 A. (You can ignore any thermal expansion of the rod.)
(a) Find the resistivity at 20.0°C
(b) Find the temperature coefficient of resistivity at 20°C for the material of the rod.
Answer: (a) 1.06 x 10^-5 Ω•m (b) 1.04 x 10^-3 K^-1

5.5
A cylindrical tungsten filament, 15.0 cm long with a diameter of 1.00 mm, is used in a machine where the temperature ranges from room temperature (20°C) up to 120°C. The filament carries a current of 12.5 A at all temperatures in this range.
(a) What will be the maximum electric field in this filament?
(b) What will be the filament’s resistance at that temperature?
(c) What will be the maximum potential drop over the full length of the filament?
Answer: (a) 1.21 V/m (b) 14.6 mΩ (c) 0.18 V

5.6
Copper cables like this one are used in high-voltage power lines to carry electricity over long distances. A copper transmission cable 100 km long and 10.0 cm in diameter carries a current of 125 A.
(a) What is the potential drop across the cable?
(b) How much electrical energy is dissipated as thermal energy every hour?
Answer: (a) 27.4 V (b) 1.23 x 10⁷ J

5.7
A resistor with resistance R consumes 0.0625 W of electrical power when connected to a 1.50-V flashlight battery. Assume R stays constant throughout this problem, even as the power consumption changes.
(a) What power does the resistor consume if it is instead connected to a 12.6-V car battery?
(b) The same resistor is connected to a different battery and consumes 5.00 W. What is the voltage of this battery?
Answer: (a) 4.4 W (b) 13 V

5.8
The power rating of a light bulb (such as a 100-W bulb) is the power it dissipates when connected across a 120-V potential difference — the standard voltage supplied by household outlets in the US.
(a) What is the resistance of a 100-W bulb
(b) What is the resistance of a 60-W bulb?
(c) How much current does each bulb draw in normal use?
Answer: (a) 144 Ω (b) 240 Ω (c) 0.83 A, 0.5 A

5.9
A heart defibrillator is used to restart the heart’s beating if it has stopped, by passing a large current through the body for a very short time. Specifically, it delivers a current of 12 A at 25 V for about 3.0 ms.
(a) What power does the defibrillator deliver to the body?
(b) How much energy is transferred?
Answer: (a) 300 W (b) 0.9 J

5.10
The battery for a certain cell phone is rated at 3.70 V. According to the manufacturer, the battery can supply 3.15 × 10⁴ J of electrical energy — enough for 5.25 h of operation — before it needs to be recharged. Find the average current that this cell phone draws when turned on.
Answer: 0.45 A