PHYS 2212 Module 5 Self Assessment Practice Problems

Module 5 Self Assessment Practice Problems

5.1
Copper has 8.5 x 10²⁸ free electrons per cubic meter. A 73.0 cm length of 12-gauge copper wire, that is 2.05 mm in diameter, carries 4.60 A of current.
(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 that carries the same current.
(c) Generally speaking, how does changing the diameter of a wire that carries a given amount of 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 (of charge +2e) and Cl^– ions (of charge –e) traveling in opposite directions.
(a) If 5.08 x 10¹⁸ Cl^– ions go from A to B every 0.580 min, while 3.20 x 10¹⁸ Ca²⁺ ions move 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 have revealed that typically about 5.6 x 10¹¹ Na⁺ ions enter each meter of the axon during a time of 10 ms. What is the current during this inflow of charge in a meter of axon?
Answer: 9 µA

5.4
A 1.50-m cylindrical rod of diameter 0.500 cm is connected to a power supply that maintains a constant potential difference of 15.0 V across its ends, while an ammeter measures the current through it. You observe that at room temperature (20.0°C) the ammeter reads 18.5 A, while 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 to be used in a machine for which the temperature will range from room temperature (20°C) up to 120°C. It will carry a current of 12.5 A at all temperatures.
(a) What will be the maximum electric field in this filament?
(b) What will be its resistance with that field?
(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
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
When a resistor with resistance R is connected to a 1.50-V flashlight battery, the resistor consumes 0.0625 W of electrical power.
(a) What power does the resistor consume if it is connected to a 12.6-V car battery? Assume that R remains constant when the power consumption changes.
(b) The resistor is connected to a 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.
(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 enable the heart to start beating if it has stopped. This is done by passing a large current of 12 A through the body at 25 V for a very short time, usually 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 it can produce 3.15 x 10⁴ J of electrical energy, enough for 5.25 h of operation, before needing to be recharged. Find the average current that this cell phone draws when turned on.
Answer: 0.45 A