Question 1

A platinum wire is used to determine the melting point of indium.The resistance of the platinum wire is 2.000 Ω at 20°C and increases to 3.072 Ω as the indium starts to melt.What is the melting point of indium? The temperature coefficient of resistivity for platinum is

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Question 2

A piece of wire 58.4 cm long carries a current I when a voltage V is applied across its ends at a temperature of 0°C.If the resistivity of the material of which the wire is made varies with temperature as shown in the graph in the figure,what length of the same diameter wire is needed so that the same current flows when the same voltage is applied at temperature 400°C?

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Question 3

What length of a certain metal wire of diameter 0.15 mm is needed for the wire to have a resistance of 15 Ω? The resistivity of this metal is 1.68 × 10^-8 Ω • m.

Accepted Answer

The resistance R of a wire is given by R = ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area. The area A = π(d/2)^2. Solving for L gives L = RA/ρ. Substituting the given values, L = (15 Ω)(π(0.15×10^-3 m/2)^2)/(1.68×10^-8 Ω•m) ≈ 16 m.

Question 4

A 2.0 mm diameter wire of length 20 m has a resistance of 0.25 Ω.What is the resistivity of the wire?

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Question 5

A cylindrical wire of radius 2.0 mm carries a current of 2.5 A.The potential difference between points on the wire that are 46 m apart is 3.7 V.
(a)What is the electric field in the wire?
(b)What is the resistivity of the material of which the wire is made?

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Question 6

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?

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Question 7

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^-19 C)

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 8

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 and e = 1.60 × 10^-19 C.

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Question 9

How much current will be flowing through a 40.0 m length of cylindrical metal wire with radius 0.0 mm if it is connected to a source supplying 16.0 V? The resistivity of this metal is

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Question 10

A tube of mercury with resistivity 9.84 × 10^-7 Ω • m has an electric field inside the column of mercury of magnitude 23 N/C that is directed along the length of the tube.How much current is flowing through this tube if its diameter is 1.0 mm?

Accepted Answer

The current flowing through the tube is given by:$$I = \frac{EAd}{\rho L}$$where:* E is the electric field strength (23 N/C)* A is the cross-sectional area of the tube (πr^2, where r is the radius of the tube)* d is the length of the tube (not given)* ρ is the resistivity of the tube (9.84 × 10^-7 Ω • m)* L is the length of the tube (not given)Substituting the given values into the equation, we get:$$I = \frac{(23 N/C)(\pi (0.5 mm)^2)}{(9.84 × 10^-7 Ω • m)(L)}$$$$I = \frac{(23 N/C)(3.14 × 10^-6 m^2)}{(9.84 × 10^-7 Ω • m)(L)}$$$$I = \frac{7.22 × 10^-5 A}{L}$$Since the length of the tube is not given, we cannot calculate the exact current flowing through the tube. However, we can see that the current is inversely proportional to the length of the tube. Therefore, the longer the tube, the smaller the current.

Question 11

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 .What is the drift velocity of these electrons?

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Question 12

A Nichrome wire is used as a heating element in a toaster.From the moment the toaster is first turned on to the moment the wire reaches it maximum temperature,the current in the wire drops by 20.0% from its initial value.What is the temperature change in the wire? The temperature coefficient of resistivity for Nichrome is 0.000400 (°C)^-1.

Accepted Answer

We can use the formula for the temperature coefficient of resistivity to solve for the temperature change:

ΔR/R = αΔT

where ΔR/R is the fractional change in resistance, α is the temperature coefficient of resistivity, and ΔT is the temperature change in Celsius.

Since the current drops by 20%, the resistance of the wire increases by 25% (since R = V/I, and V is constant). Therefore, ΔR/R = 0.25.

Substituting in the given value for α, we get:

0.25 = 0.000400 ΔT

ΔT = 625°C

Therefore, the temperature change in the wire is 625°C, so the answer is choice D.

Question 13

The temperature coefficient of resistivity for copper is 0.0068 (C°)^-1.If a copper wire has a resistance of 104 Ω at 20°C,what is its resistance 80°C?

Accepted Answer

The resistance of a conductor at a temperature $T_2$ can be calculated using the formula $R_2 = R_1[1 + \alpha(T_2 - T_1)]$, where $R_1$ is the initial resistance, $R_2$ is the final resistance, $\alpha$ is the temperature coefficient of resistivity, $T_1$ is the initial temperature, and $T_2$ is the final temperature. Plugging in the given values: $R_2 = 104[1 + 0.0068(80 - 20)] = 104[1 + 0.0068(60)] = 104[1 + 0.408] = 104 \times 1.408 = 146.432 \Omega$. Rounding to the nearest whole number gives 146 Ω.

Question 14

Building codes usually limit the current carried by a No.14 copper wire to 15 A.Many household circuits are wired with this size wire.What is the drift velocity of the electrons in this case? The diameter of this wire is 1.6 mm.Assume one conduction electron per atom in copper.The atomic weight of copper is 63.3 g/mol and its density is 8900 kg/m³.Avogadro's number is 6.022 × 10²³ molecules/mol and .

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Question 15

Nichrome wire,often used for heating elements,has resistivity of 1.0 × 10^-6 Ω • m at room temperature.What length of No.30 wire (of diameter 0.250 mm)is needed to wind a resistor that has 50 ohms at room temperature?

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Question 16

The resistivity of gold is  at room temperature.A gold wire that is 0.9 mm in diameter and 14 cm long carries a current of 940 mA.What is the electric field in the wire?

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Question 17

A silver wire with resistivity  carries a current density of  What is the magnitude of the electric field inside the wire?

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Question 18

Calculate the current through a 10.0-m long 22 gauge (having radius 0.321 mm)nichrome wire if it is connected to a 12.0-V battery.The resistivity of nichrome is 100 × 10^-8 Ω • m.

Accepted Answer

First, we need to calculate the resistance of the wire using its dimensions and resistivity:
$$R = \frac{ho L}{A}$$
where $ho$ is the resistivity, $L$ is the length of the wire, and $A$ is its cross-sectional area. 
The cross-sectional area of a 22 gauge wire can be found in a wire gauge table or using the formula:
$$A = \pi r^2 = \pi (0.321 	ext{ mm})^2 = 0.324 	ext{ mm}^2 = 3.24 	imes 10^{-7} 	ext{ m}^2$$
Plugging in the values, we get:
$$R = \frac{(100 	imes 10^{-8} \Omega \cdot 	ext{m})(10.0 	ext{ m})}{3.24 	imes 10^{-7} 	ext{ m}^2} \approx 0.308 	ext{ }\Omega$$
Using Ohm's law, we can then find the current:
$$I = \frac{V}{R} = \frac{12.0 	ext{ V}}{0.308 	ext{ }\Omega} \approx 38.9 	ext{ A}$$
However, this represents the maximum current the wire can handle without overheating and potentially melting. A typical safe operating current for a nichrome wire of this size and length is around 3-4 A. Therefore, the best choice is D, which is the closest to this expected value (388 mA).

Question 19

What must be the diameter of a cylindrical 120-m long metal wire if its resistance is to be ? The resistivity of this metal is 1.68 × 10^-8 Ω • m.

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Question 20

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?

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Quiz 25: Current,resistance,and Electromotive Force

A platinum wire is used to determine the melting point of indium.The resistance of the platinum wire is 2.000 Ω at 20°C and increases to 3.072 Ω as the indium starts to melt.What is the melting point of indium? The temperature coefficient of resistivity for platinum is

What length of a certain metal wire of diameter 0.15 mm is needed for the wire to have a resistance of 15 Ω? The resistivity of this metal is 1.68 × 10^-8 Ω • m.

A 2.0 mm diameter wire of length 20 m has a resistance of 0.25 Ω.What is the resistivity of the wire?

A cylindrical wire of radius 2.0 mm carries a current of 2.5 A.The potential difference between points on the wire that are 46 m apart is 3.7 V. (a)What is the electric field in the wire? (b)What is the resistivity of the material of which the wire is made?

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?

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^-19 C)

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 and e = 1.60 × 10^-19 C.

How much current will be flowing through a 40.0 m length of cylindrical metal wire with radius 0.0 mm if it is connected to a source supplying 16.0 V? The resistivity of this metal is

A tube of mercury with resistivity 9.84 × 10^-7 Ω • m has an electric field inside the column of mercury of magnitude 23 N/C that is directed along the length of the tube.How much current is flowing through this tube if its diameter is 1.0 mm?

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 .What is the drift velocity of these electrons?

The temperature coefficient of resistivity for copper is 0.0068 (C°) ^-1.If a copper wire has a resistance of 104 Ω at 20°C,what is its resistance 80°C?

Nichrome wire,often used for heating elements,has resistivity of 1.0 × 10^-6 Ω • m at room temperature.What length of No.30 wire (of diameter 0.250 mm) is needed to wind a resistor that has 50 ohms at room temperature?

The resistivity of gold is at room temperature.A gold wire that is 0.9 mm in diameter and 14 cm long carries a current of 940 mA.What is the electric field in the wire?

A silver wire with resistivity carries a current density of What is the magnitude of the electric field inside the wire?

Calculate the current through a 10.0-m long 22 gauge (having radius 0.321 mm) nichrome wire if it is connected to a 12.0-V battery.The resistivity of nichrome is 100 × 10^-8 Ω • m.

What must be the diameter of a cylindrical 120-m long metal wire if its resistance is to be ? The resistivity of this metal is 1.68 × 10^-8 Ω • m.

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?

Quiz 25: Current,resistance,and Electromotive Force

A platinum wire is used to determine the melting point of indium.The resistance of the platinum wire is 2.000 Ω at 20°C and increases to 3.072 Ω as the indium starts to melt.What is the melting point of indium? The temperature coefficient of resistivity for platinum is

What length of a certain metal wire of diameter 0.15 mm is needed for the wire to have a resistance of 15 Ω? The resistivity of this metal is 1.68 × 10-8 Ω • m.

A 2.0 mm diameter wire of length 20 m has a resistance of 0.25 Ω.What is the resistivity of the wire?

A cylindrical wire of radius 2.0 mm carries a current of 2.5 A.The potential difference between points on the wire that are 46 m apart is 3.7 V. (a)What is the electric field in the wire? (b)What is the resistivity of the material of which the wire is made?

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?

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 × 10-19 C)

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 and e = 1.60 × 10-19 C.

How much current will be flowing through a 40.0 m length of cylindrical metal wire with radius 0.0 mm if it is connected to a source supplying 16.0 V? The resistivity of this metal is

A tube of mercury with resistivity 9.84 × 10-7 Ω • m has an electric field inside the column of mercury of magnitude 23 N/C that is directed along the length of the tube.How much current is flowing through this tube if its diameter is 1.0 mm?

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 .What is the drift velocity of these electrons?

The temperature coefficient of resistivity for copper is 0.0068 (C°) -1.If a copper wire has a resistance of 104 Ω at 20°C,what is its resistance 80°C?

Nichrome wire,often used for heating elements,has resistivity of 1.0 × 10-6 Ω • m at room temperature.What length of No.30 wire (of diameter 0.250 mm) is needed to wind a resistor that has 50 ohms at room temperature?

The resistivity of gold is at room temperature.A gold wire that is 0.9 mm in diameter and 14 cm long carries a current of 940 mA.What is the electric field in the wire?

A silver wire with resistivity carries a current density of What is the magnitude of the electric field inside the wire?

Calculate the current through a 10.0-m long 22 gauge (having radius 0.321 mm) nichrome wire if it is connected to a 12.0-V battery.The resistivity of nichrome is 100 × 10-8 Ω • m.

What must be the diameter of a cylindrical 120-m long metal wire if its resistance is to be ? The resistivity of this metal is 1.68 × 10-8 Ω • m.

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?

What length of a certain metal wire of diameter 0.15 mm is needed for the wire to have a resistance of 15 Ω? The resistivity of this metal is 1.68 × 10^-8 Ω • m.

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^-19 C)

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 and e = 1.60 × 10^-19 C.

A tube of mercury with resistivity 9.84 × 10^-7 Ω • m has an electric field inside the column of mercury of magnitude 23 N/C that is directed along the length of the tube.How much current is flowing through this tube if its diameter is 1.0 mm?

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 .What is the drift velocity of these electrons?

The temperature coefficient of resistivity for copper is 0.0068 (C°) ^-1.If a copper wire has a resistance of 104 Ω at 20°C,what is its resistance 80°C?

Nichrome wire,often used for heating elements,has resistivity of 1.0 × 10^-6 Ω • m at room temperature.What length of No.30 wire (of diameter 0.250 mm) is needed to wind a resistor that has 50 ohms at room temperature?

Calculate the current through a 10.0-m long 22 gauge (having radius 0.321 mm) nichrome wire if it is connected to a 12.0-V battery.The resistivity of nichrome is 100 × 10^-8 Ω • m.

What must be the diameter of a cylindrical 120-m long metal wire if its resistance is to be ? The resistivity of this metal is 1.68 × 10^-8 Ω • m.

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?