Question 1

Which of the following is NOT a material property (that is, independent of the geometry)?

Accepted Answer

Current density is dependent on the specific conditions of the electrical current's flow through a material, such as the total current and the cross-sectional area through which it flows, making it not solely a material property but also geometry-dependent. Resistivity, conductivity, and density of mobile charges are intrinsic properties of materials that do not depend on the material's shape or size.

Question 2

Given two wires (with circular cross-section), one of copper having a length of 1.0 m and a diameter of 1.0 mm, the other of gold with a diameter of 2.0 mm, what length must the gold wire be in order to have the same resistance as the copper wire?

Accepted Answer

The resistance $R$ of a wire is given by $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity of the material, $L$ is the length of the wire, and $A$ is the cross-sectional area. For two wires to have the same resistance, we set their resistances equal to each other, leading to $\rho_{\text{Cu}} \frac{L_{\text{Cu}}}{A_{\text{Cu}}} = \rho_{\text{Au}} \frac{L_{\text{Au}}}{A_{\text{Au}}}$. Given that the resistivity of copper ($\rho_{\text{Cu}}$) is approximately 1.68 x 10^-8 $\Omega \cdot m$ and that of gold ($\rho_{\text{Au}}$) is approximately 2.44 x 10^-8 $\Omega \cdot m$, and using the areas calculated from the diameters (Area $A = \pi r^2$), we can solve for $L_{\text{Au}}$. The calculation shows that the gold wire needs to be approximately 2.8 times longer than the copper wire to have the same resistance, taking into account the difference in resistivity and cross-sectional area.

Question 3

By what fraction would the voltage across a nerve cell membrane drop 2.5 ms after the cell fired?

Accepted Answer

D

Question 4

Which of the following metal wires of circular cross-section, length l, and diameter d has the least resistance?

Accepted Answer

The resistance of a wire is given by the formula $R = \rho \frac{l}{A}$, where $R$ is the resistance, $\rho$ is the resistivity of the material (assumed constant for all wires since the material isn't specified), $l$ is the length of the wire, and $A$ is the cross-sectional area. The cross-sectional area of a wire with diameter $d$ is given by $A = \pi (\frac{d}{2})^2$. A wire with a shorter length and a larger cross-sectional area will have the least resistance. Among the given options, option B has a relatively short length and the largest diameter, leading to the largest cross-sectional area and thus the least resistance.

Question 5

Iron has two conductance electrons in its outer orbital shell. Its mass density is 7.87 g/cm³, and the molar mass is 55.85 g/mol. What is the drift velocity when a voltage of 12 V is applied across a 2.0 m length of iron wire?

Accepted Answer

The answer of Iron has two conductance electrons in its...

Question 6

Which of these statements is an accurate description of current?

Accepted Answer

Current is proportional to the current density, as current density is defined as the current per unit area.

Question 7

Which of the following describes how electrical current in a metal is formed?

Accepted Answer

Electrical current in a metal is formed by the slow drift motion of loosely bound electrons. These electrons are free to move within the metal's lattice structure, and when an electric field is applied, they drift in the direction opposite to the field, creating a current.

Question 8

What is the resistance of a wire made of a material with a resistivity of 3.20 × 10^-8 Ù m if its length is 3.50 m and its diameter is 0.50 mm?

Accepted Answer

The answer of What is the resistance of a wire...

Question 9

A copper wire of length 1.5 km and diameter 2 mm has a potential of 110.0 V applied across its ends. What current would an ammeter measure when placed in the circuit?

Accepted Answer

The answer of A copper wire of length 1.5 km...

Question 10

Suppose the membrane potential for a nerve cell changed from -70.0 mV to -50.0 mV. By what factor would the relative concentration of Cl^- between the axoplasm and interstitium change, given a body temperature of 37°C?

Accepted Answer

The Nernst equation, which calculates the equilibrium potential for an ion based on the concentration gradient across a membrane, can be used to solve this problem. The equation in its temperature-corrected form is: E = (RT/zF) * ln([ion]outside/[ion]inside), where E is the membrane potential, R is the gas constant, T is the temperature in Kelvin, z is the charge of the ion, F is Faraday's constant, and ln is the natural logarithm. For chloride ions (Cl-) at 37°C (or 310K), the change in membrane potential from -70.0 mV to -50.0 mV indicates a change in the driving force for chloride ions. Using the Nernst equation inversely to find the change in concentration ratio, we can calculate the factor by which the relative concentration changes. The factor is approximately 2.1, indicating that the concentration gradient of Cl- across the membrane changes by a factor of 2.1 with the given change in membrane potential.

Question 11

For any double-logarithmic plot, which one of these types of equations relating x to y gives a straight line?

Accepted Answer

A double-logarithmic plot, also known as a log-log plot, is used for equations of the form $y = ax^b$. When both x and y are plotted on logarithmic scales, this equation becomes a straight line, which is why option B is correct.

Question 12

What would happen to the decay time constant of a resting nerve cell if the membrane thickness increased?

Accepted Answer

The answer of What would happen to the decay time...

Question 13

A mass flow rate of 0.6 kg/s of cooling water is needed to remove heat from an X-ray tube operating at 3.0 MV, in which the temperature rise of the water is 30°K. What is the beam current in the X-ray tube?

Accepted Answer

The heat removed by the cooling water can be calculated using the formula $Q = mc\Delta T$, where $Q$ is the heat removed, $m$ is the mass flow rate, $c$ is the specific heat capacity of water (approximately 4.18 J/g°C), and $\Delta T$ is the temperature rise. However, for this problem, we are more interested in the electrical power absorbed by the X-ray tube, which can be calculated from the heat removed since all the electrical power is assumed to be converted into heat.Given:- Mass flow rate, $m = 0.6$ kg/s- Temperature rise, $\Delta T = 30$ K- Voltage, $V = 3.0$ MV = $3.0 \times 10^6$ VFirst, convert the mass flow rate to grams per second (since the specific heat capacity is in J/g°C) and calculate the heat removed per second (which is power, $P$):$$P = m \times c \times \Delta T$$$$P = 0.6 \times 10^3 \times 4.18 \times 30$$$$P = 75240 \, \text{W} = 75.24 \, \text{kW}$$The electrical power absorbed by the X-ray tube is equal to the product of the beam current ($I$) and the voltage ($V$):$$P = IV$$Solving for $I$:$$I = \frac{P}{V} = \frac{75.24 \times 10^3}{3.0 \times 10^6} = 0.02508 \, \text{A} = 25.08 \, \text{mA}$$Thus, the beam current in the X-ray tube is approximately 25.1 mA.

Question 14

A wire of length 3.0 m and diameter 1.5 mm has a resistance of 1.25 Ù. What is the resistivity of the material used to make the wire?

Accepted Answer

The resistivity ($\rho$) of the material can be calculated using the formula $\rho = R\frac{A}{L}$, where $R$ is the resistance, $A$ is the cross-sectional area of the wire, and $L$ is the length of the wire. The cross-sectional area $A$ of the wire, given its diameter is 1.5 mm (or 0.0015 m), is $\pi r^2 = \pi (0.0015/2)^2$ m$^2$. Substituting the given values and solving for $\rho$ yields a resistivity of approximately $7.4 \times 10^{-7}$ $\Omega m$, which corresponds to choice B.

Question 15

At what phase of the heart cycle does repolarization of the atrial chambers occur?

Accepted Answer

Repolarization of the atrial chambers occurs soon after the P-wave, which represents atrial depolarization. However, atrial repolarization is typically not visible on an ECG because it occurs during the QRS complex, which represents ventricular depolarization.

Question 16

What is the resistance of a tube of mercury of length 1.0 m and diameter 1.0 mm?

Accepted Answer

The resistance $R$ of a conductor (in this case, a tube of mercury) can be calculated using the formula $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity of the material, $L$ is the length of the conductor, and $A$ is the cross-sectional area. For mercury, $\rho$ is approximately $94 \times 10^{-8} \Omega \cdot m$. The length $L$ is given as 1.0 m, and the diameter of the tube is 1.0 mm, which means the radius $r$ is 0.5 mm or $0.5 \times 10^{-3} m$. The cross-sectional area $A$ of the tube is $\pi r^2$, which calculates to $\pi \times (0.5 \times 10^{-3})^2 m^2$. Plugging these values into the resistance formula gives a resistance close to 1.3 $\Omega$, making option A the correct choice.

Question 17

A voltage of 25.0 V is applied across a hollow iron pipe with an inner diameter of 2.0 cm and a thickness of 1.5 mm. A current of 1.5 A is measured. What is the length of the pipe?

Accepted Answer

The answer of A voltage of 25.0 V is applied...

Question 18

Which of the following properties is NOT directly accessible to experimental measurement?

Accepted Answer

Conductivity is not directly measurable; it is calculated from direct measurements of other quantities such as current, voltage, and dimensions of the material (e.g., length and cross-sectional area) using Ohm's law and its derivatives.

Question 19

What units does the constant of proportionality between speed of impulse transport and unmyelinated axon radius have?

Accepted Answer

The constant of proportionality between the speed of impulse transport and unmyelinated axon radius has units of meters per square root of seconds (m/s^1/2), which matches choice C. This is because the speed of impulse transport in unmyelinated axons is proportional to the square root of the axon radius, implying a relationship with the square root of time in the denominator for the units of speed.

Question 20

During the firing of a nerve cell, the membrane potential rises above -70 mV. The equilibrium ratio of the concentration of Cl^- ions in axoplasm to interstitium before the pulse arrives is 0.072. In which direction will the Cl^- ions flow during the passage of the pulse?

Accepted Answer

During the firing of a nerve cell, the membrane potential becomes less negative (rises above -70 mV), which can lead to a change in the direction of ion flow across the membrane. Given the equilibrium ratio of Cl- ions (represented here as Cl^- for formatting reasons) in axoplasm to interstitium is 0.072, this indicates that under resting conditions, there are more Cl- ions in the interstitium than in the axoplasm. When the membrane potential rises, the electrical gradient that normally helps retain Cl- ions in the interstitium is reduced, potentially reversing or altering the flow of ions. Therefore, Cl- ions will flow from the area of higher concentration (interstitium) to the area of lower concentration (axoplasm) to try to re-establish equilibrium, driven by both the concentration gradient and the change in membrane potential.

Quiz 18: The Flow of Charges

Which of the following is NOT a material property (that is, independent of the geometry) ?

Given two wires (with circular cross-section) , one of copper having a length of 1.0 m and a diameter of 1.0 mm, the other of gold with a diameter of 2.0 mm, what length must the gold wire be in order to have the same resistance as the copper wire?

By what fraction would the voltage across a nerve cell membrane drop 2.5 ms after the cell fired?

Which of the following metal wires of circular cross-section, length l, and diameter d has the least resistance?

Iron has two conductance electrons in its outer orbital shell. Its mass density is 7.87 g/cm³, and the molar mass is 55.85 g/mol. What is the drift velocity when a voltage of 12 V is applied across a 2.0 m length of iron wire?

Which of these statements is an accurate description of current?

Which of the following describes how electrical current in a metal is formed?

What is the resistance of a wire made of a material with a resistivity of 3.20 × 10^-8 Ù m if its length is 3.50 m and its diameter is 0.50 mm?

A copper wire of length 1.5 km and diameter 2 mm has a potential of 110.0 V applied across its ends. What current would an ammeter measure when placed in the circuit?

Suppose the membrane potential for a nerve cell changed from -70.0 mV to -50.0 mV. By what factor would the relative concentration of Cl^- between the axoplasm and interstitium change, given a body temperature of 37°C?

For any double-logarithmic plot, which one of these types of equations relating x to y gives a straight line?

What would happen to the decay time constant of a resting nerve cell if the membrane thickness increased?

A mass flow rate of 0.6 kg/s of cooling water is needed to remove heat from an X-ray tube operating at 3.0 MV, in which the temperature rise of the water is 30°K. What is the beam current in the X-ray tube?

A wire of length 3.0 m and diameter 1.5 mm has a resistance of 1.25 Ù. What is the resistivity of the material used to make the wire?

At what phase of the heart cycle does repolarization of the atrial chambers occur?

What is the resistance of a tube of mercury of length 1.0 m and diameter 1.0 mm?

A voltage of 25.0 V is applied across a hollow iron pipe with an inner diameter of 2.0 cm and a thickness of 1.5 mm. A current of 1.5 A is measured. What is the length of the pipe?

Which of the following properties is NOT directly accessible to experimental measurement?

What units does the constant of proportionality between speed of impulse transport and unmyelinated axon radius have?

During the firing of a nerve cell, the membrane potential rises above -70 mV. The equilibrium ratio of the concentration of Cl^- ions in axoplasm to interstitium before the pulse arrives is 0.072. In which direction will the Cl^- ions flow during the passage of the pulse?

Quiz 18: The Flow of Charges

Which of the following is NOT a material property (that is, independent of the geometry) ?

Given two wires (with circular cross-section) , one of copper having a length of 1.0 m and a diameter of 1.0 mm, the other of gold with a diameter of 2.0 mm, what length must the gold wire be in order to have the same resistance as the copper wire?

By what fraction would the voltage across a nerve cell membrane drop 2.5 ms after the cell fired?

Which of the following metal wires of circular cross-section, length l, and diameter d has the least resistance?

Iron has two conductance electrons in its outer orbital shell. Its mass density is 7.87 g/cm3, and the molar mass is 55.85 g/mol. What is the drift velocity when a voltage of 12 V is applied across a 2.0 m length of iron wire?

Which of these statements is an accurate description of current?

Which of the following describes how electrical current in a metal is formed?

What is the resistance of a wire made of a material with a resistivity of 3.20 × 10-8 Ù m if its length is 3.50 m and its diameter is 0.50 mm?

A copper wire of length 1.5 km and diameter 2 mm has a potential of 110.0 V applied across its ends. What current would an ammeter measure when placed in the circuit?

Suppose the membrane potential for a nerve cell changed from -70.0 mV to -50.0 mV. By what factor would the relative concentration of Cl- between the axoplasm and interstitium change, given a body temperature of 37°C?

For any double-logarithmic plot, which one of these types of equations relating x to y gives a straight line?

What would happen to the decay time constant of a resting nerve cell if the membrane thickness increased?

A mass flow rate of 0.6 kg/s of cooling water is needed to remove heat from an X-ray tube operating at 3.0 MV, in which the temperature rise of the water is 30°K. What is the beam current in the X-ray tube?

A wire of length 3.0 m and diameter 1.5 mm has a resistance of 1.25 Ù. What is the resistivity of the material used to make the wire?

At what phase of the heart cycle does repolarization of the atrial chambers occur?

What is the resistance of a tube of mercury of length 1.0 m and diameter 1.0 mm?

A voltage of 25.0 V is applied across a hollow iron pipe with an inner diameter of 2.0 cm and a thickness of 1.5 mm. A current of 1.5 A is measured. What is the length of the pipe?

Which of the following properties is NOT directly accessible to experimental measurement?

What units does the constant of proportionality between speed of impulse transport and unmyelinated axon radius have?

During the firing of a nerve cell, the membrane potential rises above -70 mV. The equilibrium ratio of the concentration of Cl- ions in axoplasm to interstitium before the pulse arrives is 0.072. In which direction will the Cl- ions flow during the passage of the pulse?

Iron has two conductance electrons in its outer orbital shell. Its mass density is 7.87 g/cm³, and the molar mass is 55.85 g/mol. What is the drift velocity when a voltage of 12 V is applied across a 2.0 m length of iron wire?

What is the resistance of a wire made of a material with a resistivity of 3.20 × 10^-8 Ù m if its length is 3.50 m and its diameter is 0.50 mm?

Suppose the membrane potential for a nerve cell changed from -70.0 mV to -50.0 mV. By what factor would the relative concentration of Cl^- between the axoplasm and interstitium change, given a body temperature of 37°C?

During the firing of a nerve cell, the membrane potential rises above -70 mV. The equilibrium ratio of the concentration of Cl^- ions in axoplasm to interstitium before the pulse arrives is 0.072. In which direction will the Cl^- ions flow during the passage of the pulse?