Problem 1
During lightning strikes from a cloud to the ground, currents as high as 25,000 A can occur and last for about 40 ms. How much charge is transferred from the cloud to the earth during such a strike?
Problem 3
A 5.00-A current runs through a 12-gauge copper wire (diameter 2.05 mm) and through a light bulb. Copper has \(8.5 \times 10^{28}\) free electrons per cubic meter. (a) How many electrons pass through the light bulb each second? (b) What is the current density in the wire? (c) At what speed does a typical electron pass by any given point in the wire? (d) If you were to use wire of twice the diameter, which of the above answers would change? Would they increase or decrease?
Problem 4
An 18-gauge copper wire (diameter 1.02 mm) carries a current with a current density of \(3.20 \times 10{^6} A/m{^2}\). The density of free electrons for copper is \(8.5 \times 10^{28}\) electrons per cubic meter. Calculate (a) the current in the wire and (b) the drift velocity of electrons in the wire.
Problem 5
Copper has \(8.5 \times 10^{28}\) free electrons per cubic meter. A 71.0-cm length of 12-gauge copper wire that is 2.05 mm in diameter carries 4.85 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?
Problem 7
The current in a wire varies with time according to the relationship \(I = 55 A\) - \(10.65 A/s{^2}2t{^2}\). (a) How many coulombs of charge pass a cross section of the wire in the time interval between \(t =\) 0 and \(t =\) 8.0 s? (b) What constant current would transport the same charge in the same time interval?
Problem 8
Current passes through a solution of sodium chloride. In 1.00 s, \(2.68 \times 10^{16}\) Na\({^+}\) ions arrive at the negative electrode and \(3.92 \times 10^{16}\) Cl\({^-}\) ions arrive at the positive electrode. (a) What is the current passing between the electrodes? (b) What is the direction of the current?
Problem 9
Nerve cells transmit electric 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 \(\times\) 10\(^{11}\) 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?
Problem 11
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\(^\circ\)C) the ammeter reads 18.5 A, while at 92.0\(^\circ\)C it reads 17.2 A. You can ignore any thermal expansion of the rod. Find (a) the resistivity at 20.0\(^\circ\)C and (b) the temperature coefficient of resistivity at 20\(^\circ\)C for the material of the rod.
Problem 12
A copper wire has a square cross section 2.3 mm on a side. The wire is 4.0 m long and carries a current of 3.6 A. The density of free electrons is 8.5 \(\times\) 10\(^{28}\)/m\({^3}\). Find the magnitudes of (a) the current density in the wire and (b) the electric field in the wire. (c) How much time is required for an electron to travel the length of the wire?
Problem 14
A wire 6.50 m long with diameter of 2.05 mm has a resistance of 0.0290 \(\Omega\). What material is the wire most likely made of?
