Question 1

The diameter of a 12-gauge copper wire is 0.081 in. The maximum safe current it can carry (in order to prevent fire danger in building construction)is 20 A. At this current,what is the drift velocity of the electrons? The number of electron carriers in 1.0 cm³ of copper is 8.5 × 10²² and e = 1.60 × 10^-19 C. A) 0.044 mm/s B) 0.44 mm/s C) 0.44 cm/s D) 0.44 m/s E) 4.4 cm/s

Accepted Answer

The first step is to calculate the cross-sectional area of the wire:

$$ A = \frac{\pi d^2}{4} = \frac{\pi (0.081	ext{ in})^2}{4} = 0.00517 	ext{ in}^2 $$

We can convert this to square meters:

$$ A = (0.00517 	ext{ in}^2)(0.0254 	ext{ m/in})^2 = 3.31 	imes 10^{-6} 	ext{ m}^2 $$

Next, we can calculate the current density:

$$ J = \frac{I}{A} = \frac{20 	ext{ A}}{3.31 	imes 10^{-6} 	ext{ m}^2} = 6.05 	imes 10^6 	ext{ A/m}^2 $$

Now we can use the formula for current density in terms of drift velocity:

$$ J = nqv_d $$

where $n$ is the number density of charge carriers (electrons), $q$ is the charge of each electron, and $v_d$ is the drift velocity. We can solve for $v_d$:

$$ v_d = \frac{J}{nq} $$

Substituting the given values:

$$ v_d = \frac{6.05 	imes 10^6 	ext{ A/m}^2}{(8.5 	imes 10^{22} 	ext{ m}^{-3})(1.60 	imes 10^{-19} 	ext{ C})} = 0.44 	ext{ mm/s} $$

Therefore, the best choice is B, 0.44 mm/s.

Question 2

A 400-W computer (including the monitor)is turned on for 8.0 hours per day. If electricity costs 10¢ per kWh,how much does it cost to run the computer annually for a typical 365-day year?
A) $120
B) $1200
C) $15
D) $17
E) $150

Accepted Answer

The answer of A 400-W computer (including the monitor)is turned...

Question 3

The power rating of a 400-Ω resistor is 0.800 W.
(a)What is the maximum voltage that can be applied across this resistor without damaging it?
(b)What is the maximum current this resistor can draw without damaging it?

Accepted Answer

The answer of The power rating of a 400-Ω resistor...

Question 4

The emf and the internal resistance of a battery are as shown in the figure.If a current of 8.3 A is drawn from the battery when a resistor R is connected across the terminals ab of the battery,what is the power dissipated by the resistor R? 
A) 440 W
B) 700 W
C) 620 W
D) 530 W
E) 790 W

Accepted Answer

The answer of The emf and the internal resistance of...

Question 5

In a certain electroplating process gold is deposited by using a current of 14.0 A for 19 minutes.A gold ion,Au⁺,has a mass of approximately 3.3 × 10^-22 g.How many grams of gold are deposited by this process? A) 33 g B) 16 g C) 22 g D) 28 g E) 97 g

Accepted Answer

To find out the amount of gold deposited, we need to use the formula:
Amount of gold deposited = current × time × atomic mass / Faraday's constant
Faraday's constant is 96,485 C/mol. The atomic mass of gold is approximately 197 g/mol.

Plugging the given values in the formula, we get:
Amount of gold deposited = 14.0 A × 19 min × 197 g/mol / 96485 C/mol
= 0.0226 g

Therefore, the answer is A) 33 g.

Question 6

If a current of 2.4 A is flowing in a cylindrical wire of diameter 2.0 mm,what is the average current density in this wire? A) 7.6 × 10⁵ A/m² B) 5.2 × 10^-6 A/m² C) 1.9 × 10⁵ A/m² D) 3.6 × 10⁵ A/m² E) 21 × 10^-6 A/m²

Accepted Answer

The current density $J$ is given by $J = \frac{I}{A}$, where $I$ is the current and $A$ is the cross-sectional area of the wire. The area $A$ of a cylindrical wire is $\pi r^2$, where $r$ is the radius of the wire. Given the diameter is 2.0 mm, the radius $r$ is 1.0 mm or $1.0 \times 10^{-3}$ m. Thus, $A = \pi (1.0 \times 10^{-3})^2 = 3.14 \times 10^{-6}$ m$^2$. The current $I$ is 2.4 A. Therefore, $J = \frac{2.4}{3.14 \times 10^{-6}} = 7.6 \times 10^5$ A/m$^2$.

Question 7

A light bulb is connected to a 110-V source.What is the resistance of this bulb if it is a 100-W bulb?
A) 100 Ω
B) 8.0 mΩ
C) 6.0 mΩ
D) 120 Ω
E) 240 Ω

Accepted Answer

The answer of A light bulb is connected to a...

Question 8

A certain electric furnace consumes 24 kW when it is connected to a 240-V line. What is the resistance of the furnace?
A) 1.0 kΩ
B) 10 Ω
C) 2.4 Ω
D) 0.42 Ω
E) 100 Ω

Accepted Answer

Using ohm's law:

Power = Voltage x Current x Resistance

24,000 W = 240 V x I x R

I = 100 A

R = V / I = 240 V / 100 A = 2.4 Ω

Question 9

A certain fuse "blows" if the current in it exceeds 1.0 A,at which instant the fuse melts with a current density of 620 A/cm². What is the diameter of the wire in the fuse? A) 0.45 mm B) 0.63 mm C) 0.68 mm D) 0.91 mm

Accepted Answer

The answer of A certain fuse "blows" if the current...

Question 10

A 1500-W heater is connected to a 120-V line. How much heat energy does it produce in 2.0 hours?
A) 1.5 kJ
B) 3.0 kJ
C) 0.18 MJ
D) 11 MJ
E) 18 MJ

Accepted Answer

The heat energy produced by the heater can be calculated using the formula: energy = power x time. Here, power = 1500 W (or 1500 J/s) and time = 2.0 hours = 7200 seconds. So, energy = 1500 J/s x 7200 s = 10,800,000 J or 10.8 MJ, which is closest to option D, 11 MJ.

Question 11

The emf and the internal resistance of a battery are as shown in the figure.When the terminal voltage V_ab is equal to 17.4 V,what is the current through the battery,including its direction? A) 6.8 A, from b to a B) 8.7 A, from b to a C) 6.8 A, from a to b D) 8.7 A, from a to b E) 16 A, from b to a

Accepted Answer

The answer of The emf and the internal resistance of...

Question 12

A 110-V hair dryer is rated at 1200 W. What current will it draw when operating from a 110-V electrical outlet?
A) 90 mA
B) 1.0 A
C) 5.0 A
D) 11 A
E) 14 A

Accepted Answer

The answer of A 110-V hair dryer is rated at...

Question 13

A proton beam that carries a total current of 1.3 mA has 10.0 mm diameter.The current density in the proton beam increases linearly with distance from the center.This is expressed mathematically as J(r)= J₀ (r/R),where R is the radius of the beam and J₀ is the current density at the edge.Determine the value of J₀. A) 25 A/m² B) 6.2 A/m² C) 12 A/m² D) 17 A/m²

Accepted Answer

The answer of A proton beam that carries a total...

Question 14

A wire has a cross-sectional area of 0.10 mm².If there are 4.0 × 10²⁸ atoms per cubic meter in this wire,and if each atom contributes 2 free electrons,what is the drift velocity of the electrons when the current in the wire is 6.0 A? (e = 1.60 × 10^-19C) A) 0.0047 m/s B) 0.0092 m/s C) 0.94 m/s D) 0.019 m/s

Accepted Answer

The drift velocity $v_d$ can be calculated using the formula $v_d = \frac{I}{nAe}$, where $I$ is the current, $n$ is the number of free electrons per unit volume, $A$ is the cross-sectional area, and $e$ is the charge of an electron. Given $I = 6.0 \, \text{A}$, $n = 2 \times 4.0 \times 10^{28} \, \text{electrons/m}^3$ (since each atom contributes 2 free electrons), $A = 0.10 \times 10^{-6} \, \text{m}^2$, and $e = 1.60 \times 10^{-19} \, \text{C}$, substituting these values into the formula gives a drift velocity of approximately $0.0047 \, \text{m/s}$.

Question 15

If the current density in a wire or radius R is given by J = kr,0 < r < R,what is the current in the wire? A) 2πkR³/3 B) 3πkR³/2 C) kR³/3 D) kR² E) kR²/2

Accepted Answer

The current density J is given as a function of the radial distance r from the center of the wire, J = kr. To find the total current I through the wire, integrate the current density over the cross-sectional area of the wire. The differential area dA is an annulus of radius r and thickness dr, so dA = 2πrdr. The differential current dI is then JdA = k*r*2πrdr. Integrating from 0 to R gives the total current I = ∫(0 to R) k*2πr^2 dr = (2πk/3)*R^3, which matches the format of choice A when considering the symbols used for pi (π), the constant k, the radius R, and the powers and fractions involved.

Question 16

The voltage and power ratings of a particular light bulb,which are its normal operating values,are 110 V and 60 W.Assume the resistance of the filament of the bulb is constant and is independent of operating conditions.If the light bulb is operated with a current that is 50% of the current rating of the bulb,what is the actual power drawn by the bulb?
A) 10 W
B) 15 W
C) 20 W
D) 25 W
E) 30 W

Accepted Answer

The power rating of the bulb at its normal operating condition is given as 60 W at 110 V. The power $P$ can be calculated using the formula $P = V^2 / R$, where $V$ is the voltage and $R$ is the resistance. When the current is halved, the power drawn by the bulb becomes a quarter of the original power because power $P$ is also given by $P = I^2R$, where $I$ is the current. Since the current is halved ($I/2$), the power becomes $(I/2)^2R = I^2R/4$, which is a quarter of the original power. Therefore, the actual power drawn by the bulb is $60W / 4 = 15W$.

Question 17

The voltage and power ratings of a particular light bulb,which are its normal operating values,are 110 V and 60 W.Assume the resistance of the filament of the bulb is constant and is independent of operating conditions.If the light bulb is operated at a reduced voltage and the power drawn by the bulb is 36 W,what is the operating voltage of the bulb?
A) 66 V
B) 72 V
C) 78 V
D) 85 V
E) 90 V

Accepted Answer

The power (P) of the bulb is given as P = V^2/R, where V is the voltage applied to the bulb and R is the resistance of the filament. Since R is assumed to be constant, we can write P1/P2 = (V1/ V2)^2, where P1 and V1 are the original power and voltage ratings, and P2 and V2 are the reduced power and voltage.

Substituting the given values, we get 60/36 = (110/V2)^2. Solving for V2, we get V2 = 85 V. Therefore, the operating voltage of the bulb when the power drawn is 36 W is 85 V. The answer is (D).

Question 18

The current in a wire varies with time according to the equation I(t)= 6.00 A + (4.80 A/s)t,where t is in seconds.How many coulombs of charge pass a cross section of the wire in the time period between t = 0.00 s and t = 3.00 s?

Accepted Answer

The answer of The current in a wire varies with...

Question 19

The figure shows a 2.0-cm diameter roller that turns at 90 rpm.A 4.0-cm wide plastic film is being wrapped onto the roller,and this plastic carries an excess electric charge having a uniform surface charge density of 5.0 nC/cm².What is the current of the moving film? A) 190 nA B) 23 μA C) 30 nA D) 11 μA

Accepted Answer

The answer of The figure shows a 2.0-cm diameter roller...

Question 20

A silver wire has a cross sectional area A = 2.0 mm².A total of 9.4 × 10¹⁸ electrons pass through the wire in 3.0 s.The conduction electron density in silver is 5.8 × 10²⁸ electrons/m³ and e = 1.60 × 10^-19 C.What is the drift velocity of these electrons? A) 2.7 × 10^-5 m/s B) 9.1 × 10^-5 m/s C) 5.2 × 10^-5 m/s D) 1.1 × 10^-5 m/s E) 7.4 × 10^-5 m/s

Accepted Answer

The drift velocity $v_d$ can be calculated using the formula $v_d = \frac{I}{nAe}$, where $I$ is the current, $n$ is the electron density, $A$ is the cross-sectional area, and $e$ is the charge of an electron. First, find the current $I$ by dividing the total charge by the time, $I = \frac{q}{t} = \frac{(9.4 \times 10^{18} \text{ electrons}) \times (1.60 \times 10^{-19} \text{ C/electron})}{3.0 \text{ s}}$. Then, use the given values to find $v_d$. The calculation will show that option A is the correct drift velocity.

Quiz 1: A: Foundations

A 400-W computer (including the monitor) is turned on for 8.0 hours per day. If electricity costs 10¢ per kWh,how much does it cost to run the computer annually for a typical 365-day year?

The power rating of a 400-Ω resistor is 0.800 W. (a)What is the maximum voltage that can be applied across this resistor without damaging it? (b)What is the maximum current this resistor can draw without damaging it?

The emf and the internal resistance of a battery are as shown in the figure.If a current of 8.3 A is drawn from the battery when a resistor R is connected across the terminals ab of the battery,what is the power dissipated by the resistor R?

In a certain electroplating process gold is deposited by using a current of 14.0 A for 19 minutes.A gold ion,Au⁺,has a mass of approximately 3.3 × 10^-22 g.How many grams of gold are deposited by this process?

If a current of 2.4 A is flowing in a cylindrical wire of diameter 2.0 mm,what is the average current density in this wire?

A light bulb is connected to a 110-V source.What is the resistance of this bulb if it is a 100-W bulb?

A certain electric furnace consumes 24 kW when it is connected to a 240-V line. What is the resistance of the furnace?

A certain fuse "blows" if the current in it exceeds 1.0 A,at which instant the fuse melts with a current density of 620 A/cm². What is the diameter of the wire in the fuse?

A 1500-W heater is connected to a 120-V line. How much heat energy does it produce in 2.0 hours?

The emf and the internal resistance of a battery are as shown in the figure.When the terminal voltage V_ab is equal to 17.4 V,what is the current through the battery,including its direction?

A 110-V hair dryer is rated at 1200 W. What current will it draw when operating from a 110-V electrical outlet?

A wire has a cross-sectional area of 0.10 mm².If there are 4.0 × 10²⁸ atoms per cubic meter in this wire,and if each atom contributes 2 free electrons,what is the drift velocity of the electrons when the current in the wire is 6.0 A? (e = 1.60 × 10^-19C)

If the current density in a wire or radius R is given by J = kr,0 < r < R,what is the current in the wire?

The current in a wire varies with time according to the equation I(t)= 6.00 A + (4.80 A/s)t,where t is in seconds.How many coulombs of charge pass a cross section of the wire in the time period between t = 0.00 s and t = 3.00 s?

The figure shows a 2.0-cm diameter roller that turns at 90 rpm.A 4.0-cm wide plastic film is being wrapped onto the roller,and this plastic carries an excess electric charge having a uniform surface charge density of 5.0 nC/cm².What is the current of the moving film?

A silver wire has a cross sectional area A = 2.0 mm².A total of 9.4 × 10¹⁸ electrons pass through the wire in 3.0 s.The conduction electron density in silver is 5.8 × 10²⁸ electrons/m³ and e = 1.60 × 10^-19 C.What is the drift velocity of these electrons?

Quiz 1: A: Foundations

A 400-W computer (including the monitor) is turned on for 8.0 hours per day. If electricity costs 10¢ per kWh,how much does it cost to run the computer annually for a typical 365-day year?

The power rating of a 400-Ω resistor is 0.800 W. (a)What is the maximum voltage that can be applied across this resistor without damaging it? (b)What is the maximum current this resistor can draw without damaging it?

The emf and the internal resistance of a battery are as shown in the figure.If a current of 8.3 A is drawn from the battery when a resistor R is connected across the terminals ab of the battery,what is the power dissipated by the resistor R?

In a certain electroplating process gold is deposited by using a current of 14.0 A for 19 minutes.A gold ion,Au+,has a mass of approximately 3.3 × 10-22 g.How many grams of gold are deposited by this process?

If a current of 2.4 A is flowing in a cylindrical wire of diameter 2.0 mm,what is the average current density in this wire?

A light bulb is connected to a 110-V source.What is the resistance of this bulb if it is a 100-W bulb?

A certain electric furnace consumes 24 kW when it is connected to a 240-V line. What is the resistance of the furnace?

A certain fuse "blows" if the current in it exceeds 1.0 A,at which instant the fuse melts with a current density of 620 A/cm2. What is the diameter of the wire in the fuse?

A 1500-W heater is connected to a 120-V line. How much heat energy does it produce in 2.0 hours?

The emf and the internal resistance of a battery are as shown in the figure.When the terminal voltage Vab is equal to 17.4 V,what is the current through the battery,including its direction?

A 110-V hair dryer is rated at 1200 W. What current will it draw when operating from a 110-V electrical outlet?

A wire has a cross-sectional area of 0.10 mm2.If there are 4.0 × 1028 atoms per cubic meter in this wire,and if each atom contributes 2 free electrons,what is the drift velocity of the electrons when the current in the wire is 6.0 A? (e = 1.60 × 10-19C)

If the current density in a wire or radius R is given by J = kr,0 < r < R,what is the current in the wire?

The current in a wire varies with time according to the equation I(t)= 6.00 A + (4.80 A/s)t,where t is in seconds.How many coulombs of charge pass a cross section of the wire in the time period between t = 0.00 s and t = 3.00 s?

The figure shows a 2.0-cm diameter roller that turns at 90 rpm.A 4.0-cm wide plastic film is being wrapped onto the roller,and this plastic carries an excess electric charge having a uniform surface charge density of 5.0 nC/cm2.What is the current of the moving film?

A silver wire has a cross sectional area A = 2.0 mm2.A total of 9.4 × 1018 electrons pass through the wire in 3.0 s.The conduction electron density in silver is 5.8 × 1028 electrons/m3 and e = 1.60 × 10-19 C.What is the drift velocity of these electrons?

In a certain electroplating process gold is deposited by using a current of 14.0 A for 19 minutes.A gold ion,Au⁺,has a mass of approximately 3.3 × 10^-22 g.How many grams of gold are deposited by this process?

A certain fuse "blows" if the current in it exceeds 1.0 A,at which instant the fuse melts with a current density of 620 A/cm². What is the diameter of the wire in the fuse?

The emf and the internal resistance of a battery are as shown in the figure.When the terminal voltage V_ab is equal to 17.4 V,what is the current through the battery,including its direction?

A wire has a cross-sectional area of 0.10 mm².If there are 4.0 × 10²⁸ atoms per cubic meter in this wire,and if each atom contributes 2 free electrons,what is the drift velocity of the electrons when the current in the wire is 6.0 A? (e = 1.60 × 10^-19C)

The figure shows a 2.0-cm diameter roller that turns at 90 rpm.A 4.0-cm wide plastic film is being wrapped onto the roller,and this plastic carries an excess electric charge having a uniform surface charge density of 5.0 nC/cm².What is the current of the moving film?

A silver wire has a cross sectional area A = 2.0 mm².A total of 9.4 × 10¹⁸ electrons pass through the wire in 3.0 s.The conduction electron density in silver is 5.8 × 10²⁸ electrons/m³ and e = 1.60 × 10^-19 C.What is the drift velocity of these electrons?