Resistivity
Q. A copper wire has a resistivity of 1.68 x 10^-8 Ω·m. What is the resistance of a 100 m long wire with a cross-sectional area of 1 mm²?
A.
1.68 Ω
B.
0.168 Ω
C.
0.0168 Ω
D.
16.8 Ω
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Solution
Resistance (R) = ρ * (L / A) = 1.68 x 10^-8 * (100 / 1 x 10^-6) = 1.68 Ω.
Correct Answer: A — 1.68 Ω
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Q. A cylindrical conductor has a length L and radius r. If the radius is doubled while keeping the length constant, how does the resistivity change?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Increases four times
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Solution
Resistivity is an intrinsic property of the material and does not change with geometry.
Correct Answer: C — Remains the same
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Q. A cylindrical conductor has a length of 1 m and a radius of 0.01 m. If its resistivity is 2 x 10^-8 Ω·m, what is its resistance?
A.
0.01 Ω
B.
0.02 Ω
C.
0.03 Ω
D.
0.04 Ω
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Solution
Resistance R = ρ * (L / A) = 2 x 10^-8 * (1 / (π * (0.01)²)) = 0.02 Ω.
Correct Answer: B — 0.02 Ω
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Q. A cylindrical wire has a length of 1 m and a radius of 0.5 mm. If its resistivity is 1.68 x 10^-8 Ω·m, what is its resistance?
A.
0.0212 Ω
B.
0.0424 Ω
C.
0.0848 Ω
D.
0.168 Ω
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Solution
Resistance R = ρ(L/A) = 1.68 x 10^-8 * (1 / (π(0.5 x 10^-3)²)) = 0.0424 Ω.
Correct Answer: B — 0.0424 Ω
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Q. A wire has a resistance of 10 ohms at 20°C. If the temperature coefficient of resistivity is 0.004/°C, what will be its resistance at 100°C?
A.
10.4 ohms
B.
12 ohms
C.
14 ohms
D.
16 ohms
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Solution
R = R0(1 + α(T - T0)) = 10(1 + 0.004(100 - 20)) = 10(1 + 0.32) = 10.4 ohms.
Correct Answer: B — 12 ohms
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Q. A wire has a resistance of 10 Ω at 20°C. If the temperature coefficient of resistivity is 0.004/°C, what will be the resistance at 100°C?
A.
10 Ω
B.
12 Ω
C.
14 Ω
D.
16 Ω
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Solution
R = R0(1 + α(T - T0)) = 10(1 + 0.004(100 - 20)) = 10(1 + 0.32) = 10(1.32) = 13.2 Ω.
Correct Answer: C — 14 Ω
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Q. A wire has a resistance of 10 Ω at 20°C. If the temperature coefficient of resistivity is 0.004/°C, what will be its resistance at 100°C?
A.
10 Ω
B.
12 Ω
C.
14 Ω
D.
16 Ω
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Solution
R = R0(1 + α(T - T0)) = 10(1 + 0.004(100 - 20)) = 10(1 + 0.32) = 10(1.32) = 13.2 Ω.
Correct Answer: C — 14 Ω
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Q. A wire has a resistance of 12 Ω and is made of a material with a resistivity of 3 x 10^-6 Ω·m. If the length of the wire is 4 m, what is its cross-sectional area?
A.
0.5 mm²
B.
1 mm²
C.
2 mm²
D.
3 mm²
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Solution
A = ρ * (L / R) = 3 x 10^-6 * (4 / 12) = 1 mm².
Correct Answer: B — 1 mm²
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Q. A wire has a resistance of 5 Ω at 20°C. If the temperature coefficient of resistivity is 0.004/°C, what will be its resistance at 100°C?
A.
5.4 Ω
B.
6.4 Ω
C.
7.4 Ω
D.
8.4 Ω
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Solution
R = R0(1 + α(T - T0)) = 5(1 + 0.004(100 - 20)) = 6.4 Ω.
Correct Answer: B — 6.4 Ω
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Q. A wire made of material A has a resistivity of 1.5 x 10^-8 Ω·m, while material B has a resistivity of 3.0 x 10^-8 Ω·m. If both wires have the same dimensions, which wire will have a higher resistance?
A.
Wire A
B.
Wire B
C.
Both have the same resistance
D.
Cannot be determined
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Solution
Resistance is directly proportional to resistivity; hence, wire B with higher resistivity will have higher resistance.
Correct Answer: B — Wire B
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Q. A wire made of material A has twice the length and half the cross-sectional area of a wire made of material B. If the resistivity of A is ρ, what is the resistance of wire A in terms of the resistance of wire B?
A.
2R
B.
4R
C.
R/2
D.
R/4
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Solution
Resistance R = ρ(L/A). For wire A, R_A = ρ(2L/(A/2)) = 4ρ(L/A) = 4R_B.
Correct Answer: B — 4R
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Q. A wire of length 10 m and cross-sectional area 2 mm² has a resistance of 3 Ω. What is the resistivity of the material?
A.
1.5 x 10^-6 Ω·m
B.
3 x 10^-6 Ω·m
C.
6 x 10^-6 Ω·m
D.
1.5 x 10^-5 Ω·m
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Solution
Resistivity ρ = R * (A / L) = 3 * (2 x 10^-6 / 10) = 1.5 x 10^-6 Ω·m.
Correct Answer: A — 1.5 x 10^-6 Ω·m
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Q. If a wire's length is doubled while keeping its cross-sectional area constant, how does its resistance change?
A.
Remains the same
B.
Doubles
C.
Halves
D.
Quadruples
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Solution
Resistance is directly proportional to length; doubling the length doubles the resistance.
Correct Answer: B — Doubles
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Q. If the cross-sectional area of a wire is doubled, how does its resistance change?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Increases four times
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Solution
Resistance is inversely proportional to cross-sectional area; doubling the area halves the resistance.
Correct Answer: B — Halves
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Q. If the cross-sectional area of a wire is doubled, what happens to its resistance?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Increases four times
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Solution
Resistance (R) is inversely proportional to cross-sectional area (A). Doubling A halves the resistance.
Correct Answer: B — Halves
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Q. If the length of a wire is doubled while keeping the cross-sectional area constant, how does its resistance change?
A.
Remains the same
B.
Doubles
C.
Halves
D.
Quadruples
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Solution
Resistance is directly proportional to length; doubling the length doubles the resistance.
Correct Answer: B — Doubles
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Q. If the resistivity of a material is 1.5 x 10^-8 Ω·m, what is the resistance of a 3 m long wire with a cross-sectional area of 0.5 mm²?
A.
0.09 Ω
B.
0.18 Ω
C.
0.27 Ω
D.
0.36 Ω
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Solution
Resistance R = ρ(L/A) = (1.5 x 10^-8)(3)/(0.5 x 10^-6) = 0.09 Ω.
Correct Answer: B — 0.18 Ω
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Q. If the resistivity of a material is 2 x 10^-8 Ω·m and the wire has a length of 3 m and a cross-sectional area of 0.5 mm², what is the resistance?
A.
0.12 Ω
B.
0.15 Ω
C.
0.18 Ω
D.
0.20 Ω
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Solution
Resistance R = ρ * (L / A) = 2 x 10^-8 * (3 / 0.5 x 10^-6) = 0.12 Ω.
Correct Answer: A — 0.12 Ω
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Q. If the resistivity of a material is doubled, what happens to the resistance of a wire of constant length and cross-sectional area?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
Resistance R is directly proportional to resistivity ρ, so if ρ is doubled, R also doubles.
Correct Answer: A — It doubles
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Q. If the resistivity of a material is halved, what happens to the resistance of a uniform wire of that material?
A.
Halved
B.
Doubled
C.
Remains the same
D.
Quadrupled
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Solution
Resistance is directly proportional to resistivity; halving resistivity halves the resistance.
Correct Answer: A — Halved
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Q. If the resistivity of a material is halved, what happens to the resistance of a wire of fixed length and cross-sectional area?
A.
Halved
B.
Doubled
C.
Remains the same
D.
Quadrupled
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Solution
Resistance is directly proportional to resistivity; halving resistivity halves the resistance.
Correct Answer: A — Halved
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Q. If the resistivity of a material is halved, what will happen to the resistance of a wire of fixed length and cross-sectional area?
A.
Halved
B.
Doubled
C.
Remains the same
D.
Quadrupled
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Solution
Resistance is directly proportional to resistivity; halving resistivity halves the resistance.
Correct Answer: A — Halved
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Q. If the resistivity of a superconductor is zero, what can be said about its resistance?
A.
Infinite
B.
Zero
C.
Depends on temperature
D.
Undefined
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Solution
A superconductor has zero resistivity, which means it has zero resistance.
Correct Answer: B — Zero
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Q. If the resistivity of copper is 1.68 x 10^-8 Ω·m, what is the resistance of a copper wire of length 100 m and diameter 1 mm?
A.
0.168 Ω
B.
0.168 kΩ
C.
1.68 Ω
D.
1.68 kΩ
Show solution
Solution
Resistance R = ρ * (L / A) = 1.68 x 10^-8 * (100 / (π * (0.5 x 10^-3)²)) = 0.168 Ω.
Correct Answer: A — 0.168 Ω
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Q. If the temperature of a conductor increases, what happens to its resistivity?
A.
Increases
B.
Decreases
C.
Remains constant
D.
Depends on the material
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Solution
For most conductors, resistivity increases with temperature due to increased atomic vibrations.
Correct Answer: A — Increases
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Q. If the temperature of a metallic conductor increases, what happens to its resistivity?
A.
Increases
B.
Decreases
C.
Remains constant
D.
Becomes zero
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Solution
For metals, resistivity increases with temperature due to increased lattice vibrations.
Correct Answer: A — Increases
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Q. If two resistors of resistivity 5 x 10^-6 Ω·m are connected in series, what is the total resistivity?
A.
5 x 10^-6 Ω·m
B.
10 x 10^-6 Ω·m
C.
2.5 x 10^-6 Ω·m
D.
None of the above
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Solution
Resistivity is a property of the material, not the configuration; it remains 5 x 10^-6 Ω·m.
Correct Answer: A — 5 x 10^-6 Ω·m
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Q. If two resistors of resistivity 5 Ω·m and 10 Ω·m are connected in series, what is the total resistance?
A.
15 Ω
B.
5 Ω
C.
10 Ω
D.
20 Ω
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Solution
Total resistance in series is the sum: R_total = R1 + R2 = 5 + 10 = 15 Ω.
Correct Answer: A — 15 Ω
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Q. If two resistors of resistivity ρ are connected in series, what is the total resistivity of the combination?
A.
ρ
B.
2ρ
C.
ρ/2
D.
Depends on the configuration
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Solution
Resistivity is a property of the material and does not change with series or parallel connections.
Correct Answer: A — ρ
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Q. In a material with a resistivity of 2 x 10^-8 Ω·m, what is the resistance of a 10 m long wire with a cross-sectional area of 1 mm²?
A.
0.02 Ω
B.
0.2 Ω
C.
2 Ω
D.
20 Ω
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Solution
Resistance R = ρ(L/A) = 2 x 10^-8 * (10 / (1 x 10^-6)) = 0.2 Ω.
Correct Answer: B — 0.2 Ω
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