Resistivity
Q. If two resistors of resistivity ρ are connected in series, what is the total resistivity of the combination?
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A.
ρ
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B.
2ρ
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C.
ρ/2
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D.
Depends on the configuration
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. If two wires of the same material are connected in series, how does their combined resistance compare to the individual resistances?
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A.
Less than both
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B.
Equal to the sum
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C.
Greater than both
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D.
Depends on length
Solution
In series, the total resistance is the sum of individual resistances.
Correct Answer: B — Equal to the sum
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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?
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A.
0.02 Ω
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B.
0.2 Ω
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C.
2 Ω
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D.
20 Ω
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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Q. In a material with a resistivity of 2 x 10^-8 Ω·m, what is the resistance of a 3 m long wire with a cross-sectional area of 1 mm²?
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A.
0.006 Ω
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B.
0.018 Ω
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C.
0.024 Ω
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D.
0.036 Ω
Solution
Resistance R = ρ(L/A) = 2 x 10^-8 * (3 / (1 x 10^-6)) = 0.024 Ω.
Correct Answer: C — 0.024 Ω
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Q. In a series circuit, if one resistor has a resistance of 5 Ω and another has 10 Ω, what is the total resistance?
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A.
5 Ω
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B.
10 Ω
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C.
15 Ω
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D.
20 Ω
Solution
In a series circuit, total resistance R_total = R1 + R2 = 5 Ω + 10 Ω = 15 Ω.
Correct Answer: C — 15 Ω
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Q. In a series circuit, if one resistor has a resistivity of 5 Ω·m and another has 10 Ω·m, what is the total resistance?
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A.
5 Ω
-
B.
10 Ω
-
C.
15 Ω
-
D.
20 Ω
Solution
In series, total resistance R_total = R1 + R2 = 5 + 10 = 15 Ω.
Correct Answer: C — 15 Ω
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Q. In a temperature-resistivity graph, what does the slope represent for a metallic conductor?
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A.
Resistivity
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B.
Temperature coefficient of resistivity
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C.
Resistance
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D.
Conductivity
Solution
The slope of the temperature-resistivity graph represents the temperature coefficient of resistivity.
Correct Answer: B — Temperature coefficient of resistivity
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Q. What happens to the resistance of a wire if its diameter is halved while keeping the length constant?
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A.
It doubles
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B.
It halves
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C.
It quadruples
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D.
It remains the same
Solution
Resistance R is inversely proportional to the area; halving the diameter quarters the area, thus quadrupling the resistance.
Correct Answer: C — It quadruples
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Q. What happens to the resistivity of a superconductor as it approaches absolute zero?
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A.
Increases
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B.
Decreases
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C.
Becomes infinite
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D.
Becomes zero
Solution
The resistivity of a superconductor approaches zero as it reaches absolute zero.
Correct Answer: D — Becomes zero
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Q. What happens to the resistivity of a superconductor as it transitions to the superconducting state?
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A.
Increases
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B.
Decreases
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C.
Becomes zero
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D.
Remains constant
Solution
In the superconducting state, the resistivity of a superconductor becomes zero.
Correct Answer: C — Becomes zero
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Q. What happens to the total resistance in a parallel circuit if more resistors are added?
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A.
Increases
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B.
Decreases
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C.
Remains constant
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D.
Depends on the resistors
Solution
In a parallel circuit, adding more resistors decreases the total resistance.
Correct Answer: B — Decreases
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Q. What happens to the total resistance in a parallel circuit if one of the resistors is removed?
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A.
Increases
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B.
Decreases
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C.
Remains the same
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D.
Depends on the other resistors
Solution
Removing a resistor in parallel increases the total resistance, as there are fewer paths for current.
Correct Answer: A — Increases
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Q. What is the effect of increasing the cross-sectional area of a conductor on its resistance?
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A.
Increases resistance
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B.
Decreases resistance
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C.
No effect
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D.
Depends on the material
Solution
Increasing the cross-sectional area decreases the resistance, as R = ρ * (L / A).
Correct Answer: B — Decreases resistance
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Q. What is the effect of increasing the length of a conductor on its resistance?
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A.
Increases resistance
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B.
Decreases resistance
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C.
No effect
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D.
Depends on the material
Solution
Resistance (R) is directly proportional to length (L); increasing length increases resistance.
Correct Answer: A — Increases resistance
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Q. What is the effect of increasing the length of a conductor on its resistivity?
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A.
Increases
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B.
Decreases
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C.
No effect
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D.
Depends on the material
Solution
Resistivity is an intrinsic property of the material and does not change with length.
Correct Answer: C — No effect
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Q. What is the resistivity of a material if a 5 m long wire with a cross-sectional area of 1 mm² has a resistance of 10 Ω?
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A.
2 x 10^-6 Ω·m
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B.
5 x 10^-6 Ω·m
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C.
1 x 10^-5 Ω·m
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D.
2 x 10^-5 Ω·m
Solution
Resistivity ρ = R * (A / L) = 10 * (1 x 10^-6 / 5) = 2 x 10^-5 Ω·m.
Correct Answer: C — 1 x 10^-5 Ω·m
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Q. What is the resistivity of a material if a wire of length 2 m and cross-sectional area 1 mm² has a resistance of 4 ohms?
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A.
2 x 10^-6 Ω·m
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B.
4 x 10^-6 Ω·m
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C.
8 x 10^-6 Ω·m
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D.
1 x 10^-6 Ω·m
Solution
Resistivity (ρ) = R * (A / L) = 4 * (1 x 10^-6 / 2) = 4 x 10^-6 Ω·m.
Correct Answer: B — 4 x 10^-6 Ω·m
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Q. What is the unit of resistivity?
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A.
Ohm
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B.
Ohm-meter
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C.
Siemens
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D.
Coulomb
Solution
The unit of resistivity is Ohm-meter (Ω·m).
Correct Answer: B — Ohm-meter
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Q. Which material has the highest resistivity?
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A.
Copper
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B.
Aluminum
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C.
Iron
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D.
Rubber
Solution
Rubber has a much higher resistivity compared to metals like copper, aluminum, and iron.
Correct Answer: D — Rubber
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Q. Which material has the lowest resistivity?
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A.
Copper
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B.
Aluminum
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C.
Silver
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D.
Iron
Solution
Silver has the lowest resistivity among common materials.
Correct Answer: C — Silver
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Q. Which of the following factors does NOT affect the resistivity of a material?
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A.
Temperature
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B.
Material type
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C.
Length of the conductor
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D.
Cross-sectional area
Solution
Resistivity is a property of the material and does not depend on the length or cross-sectional area.
Correct Answer: C — Length of the conductor
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Q. Which of the following materials has the highest resistivity?
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A.
Copper
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B.
Aluminum
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C.
Silver
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D.
Rubber
Solution
Rubber is an insulator and has a much higher resistivity compared to metals like copper, aluminum, and silver.
Correct Answer: D — Rubber
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