Which statement correctly describes the resistivity of a wire?(1 point)
A.) Resistivity depends on the current through the wire and has units of ohms.
B.) Resistivity depends on the material the wire is made from and has units of ohm-meters.
C.) Resistivity depends on the material the wire is made from and has units of ohms.
D.) Resistivity depends on the current through the wire and has units of ohm-meters.
Which representation shows the relationship between resistance and the length of a wire?(1 point)
A.) R∝LR∝L
B.) R∝1LR∝1L
C.) R∝L2R∝L2
D.) R∝1L2
The table shows the resistivity of four different materials.
Material
Resistivity (Ω⋅m)
Aluminum 2.65 x 10–8
Copper 1.68 x 10–8
Silver 1.59 x 10–8
Tungsten 5.60 x 10–8
About how many times greater is the resistance of a tungsten wire than the resistance of a silver wire of the same length and cross-sectional area? (1 point)
A.) 0.28
B.) 3.52
C.) 2.11
D.) 3.33
The resistance of a wire is 8 Ω. What would the resistance be if the length of the wire was increased by a factor of four?(1 point)
A.) 32 Ω
B.) 16 Ω
C.) 2 Ω
D.) 4 Ω
What current is produced with a voltage of 6.0 V and a resistance of 445 ohms?(1 point)
A.) 17.4 mA
B.) 11.0 mA
C.) 15.7 mA
D.) 13.5 mA
Suppose wire X and wire Y are made of different materials, and have different lengths and cross-sectional areas. What is the ratio of the resistance of wire X to the resistance of wire Y?
The length of wire X is one fifth the length of wire Y.
The radius of wire X is one third the radius of wire Y.
The resistivity of the material of wire X is half the resistivity of the material of wire Y.
(1 point)
A.) 9:10
B.) 10:9
C.) 10:3
D.) 3:10
1-Resistivity depends on the material the wire is made from and has units of ohm-meters.
2-R∝L
3-3.52
4-32 Ω
5-13.5 mA
6-9:10
A.) Resistivity depends on the material the wire is made from and has units of ohm-meters.
C.) R∝L
B.) 3.52
A.) 32 Ω
B.) 11.0 mA
B.) 10:9
The correct answers are:
A.) Resistivity depends on the material the wire is made from and has units of ohm-meters.
B.) R∝L
D.) 3.33
A.) 32 Ω
C.) 15.7 mA
B.) 10:9
The correct answer for the first question is B.) Resistivity depends on the material the wire is made from and has units of ohm-meters. To understand this, we need to know that resistivity is a property of a material and is independent of the current through the wire. It measures how much a material opposes the flow of electric current. Resistivity is represented by the Greek letter "rho" (ρ) and is measured in ohm-meters (Ω⋅m).
For the second question, the correct answer is A.) R∝L. The relationship between resistance (R) and the length of a wire (L) is directly proportional (R∝L). This means that as the length of the wire increases, so does its resistance.
To answer the third question, we can compare the resistivity values of tungsten and silver given in the table. The resistivity of tungsten is 5.60 x 10^(-8) Ω⋅m and the resistivity of silver is 1.59 x 10^(-8) Ω⋅m. To find how many times greater the resistance of tungsten is compared to silver, we divide their resistivity values.
(5.60 x 10^(-8) Ω⋅m) / (1.59 x 10^(-8) Ω⋅m) ≈ 3.52
Therefore, the answer is B.) 3.52. The resistance of a tungsten wire is about 3.52 times greater than the resistance of a silver wire of the same length and cross-sectional area.
To answer the fourth question, we need to understand the relationship between resistance and the length of a wire. Since the resistance of a wire is directly proportional to its length (R∝L), if the length of the wire is increased by a factor of four, the resistance will also increase by the same factor. Therefore, the new resistance will be 4 times the original resistance.
Original resistance = 8 Ω
Increased resistance = 4 * 8 Ω = 32 Ω
So, the answer is A.) 32 Ω.
To answer the fifth question, we can use Ohm's Law, which states that the current (I) flowing through a circuit is equal to the voltage (V) divided by the resistance (R). Using the given values:
Voltage (V) = 6.0 V
Resistance (R) = 445 Ω
Current (I) = V / R = 6.0 V / 445 Ω ≈ 0.0135 A
To convert the current to milliamperes (mA), we multiply by 1000:
Current (I) = 0.0135 A * 1000 = 13.5 mA
So, the answer is D.) 13.5 mA.
For the final question, we need to analyze the given information about wire X and wire Y. The length of wire X is one fifth (1/5) the length of wire Y, the radius of wire X is one third (1/3) the radius of wire Y, and the resistivity of the material of wire X is half (1/2) the resistivity of the material of wire Y.
We know that resistance is directly proportional to both the length of the wire and the resistivity of the material, and inversely proportional to the cross-sectional area (which is related to the radius squared). Let's define the resistance ratios as:
Ratio of resistance of wire X to wire Y = R_X / R_Y
From the given information, we can determine the relationships:
R_X ∝ L_X
R_Y ∝ L_Y
R_X ∝ 1 / A_X
R_Y ∝ 1 / A_Y
R_X ∝ ρ_X
R_Y ∝ ρ_Y
Now let's look at the ratios:
R_X / R_Y = (L_X / L_Y) * (1 / A_X) * ρ_X / (1 / A_Y) * ρ_Y
Using the given fractions and ratios:
(L_X / L_Y) = 1/5
(A_X / A_Y) = (1/3)^2 = 1/9
(ρ_X / ρ_Y) = 1/2
Substituting these values in:
R_X / R_Y = (1/5) * (9/1) * (1/2) = 9/10
Therefore, the answer is A.) 9:10. The ratio of the resistance of wire X to the resistance of wire Y is 9:10.