Current Electricity
Q. If the resistance values in a Wheatstone bridge are all equal, what is the condition for balance?
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A.
All resistances must be zero
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B.
Any resistance can be changed
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C.
The bridge is always balanced
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D.
The bridge is never balanced
Solution
If all resistances are equal, the bridge is always balanced regardless of the values.
Correct Answer: C — The bridge is always balanced
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Q. If the resistance values in a Wheatstone bridge are doubled, what happens to the balance condition?
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A.
It remains the same
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B.
It becomes unbalanced
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C.
It becomes easier to balance
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D.
It becomes impossible to balance
Solution
Doubling all resistance values does not affect the balance condition, as the ratios remain the same.
Correct Answer: A — It remains the same
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Q. If the resistance values in a Wheatstone bridge are R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, what should R4 be for the bridge to be balanced?
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A.
7.5Ω
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B.
10Ω
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C.
12.5Ω
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D.
15Ω
Solution
Using the balance condition R1/R2 = R3/R4, we find R4 = (R2 * R3) / R1 = (15 * 5) / 10 = 7.5Ω.
Correct Answer: C — 12.5Ω
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Q. If the resistance values in a Wheatstone bridge are R1 = 10Ω, R2 = 20Ω, R3 = 15Ω, what is the value of R4 for the bridge to be balanced?
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A.
30Ω
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B.
15Ω
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C.
10Ω
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D.
5Ω
Solution
Using the balance condition R1/R2 = R3/R4, we find R4 = (R2 * R3) / R1 = (20 * 15) / 10 = 30Ω.
Correct Answer: B — 15Ω
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Q. If the resistances in a Wheatstone bridge are 10Ω, 20Ω, 30Ω, and 60Ω, what is the value of the unknown resistance?
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A.
15Ω
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B.
25Ω
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C.
30Ω
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D.
45Ω
Solution
Using the formula R1/R2 = R3/R4, we find that R4 = (R2 * R3) / R1 = (20 * 30) / 10 = 60Ω.
Correct Answer: B — 25Ω
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Q. If the resistances in a Wheatstone bridge are 4Ω, 8Ω, 12Ω, and R, what is the value of R for the bridge to be balanced?
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A.
6Ω
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B.
8Ω
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C.
10Ω
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D.
12Ω
Solution
Using the balance condition R1/R2 = R3/R4, we find R = (R2 * R3) / R1 = (8 * 12) / 4 = 24Ω.
Correct Answer: A — 6Ω
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Q. If the resistances in a Wheatstone bridge are 5Ω, 15Ω, 10Ω, and R, what is the value of R for the bridge to be balanced?
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A.
7.5Ω
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B.
10Ω
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C.
12.5Ω
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D.
15Ω
Solution
Using the balance condition R1/R2 = R3/R4, we find R = (R2 * R3) / R1 = (15 * 10) / 5 = 30Ω.
Correct Answer: C — 12.5Ω
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Q. If the resistances in a Wheatstone bridge are equal, what is the current through the galvanometer?
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A.
Zero
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B.
Maximum
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C.
Minimum
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D.
Depends on the voltage
Solution
If all resistances are equal, the bridge is balanced and the current through the galvanometer is zero.
Correct Answer: A — Zero
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Q. If the resistances in a Wheatstone bridge are equal, what is the potential difference across the galvanometer?
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A.
Zero
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B.
Equal to the supply voltage
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C.
Half of the supply voltage
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D.
Depends on the resistances
Solution
If the resistances are equal, the potential difference across the galvanometer is zero.
Correct Answer: A — Zero
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Q. If the resistances in a Wheatstone bridge are P = 10Ω, Q = 15Ω, R = 5Ω, and S = xΩ, what is the value of x for the bridge to be balanced?
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A.
7.5Ω
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B.
10Ω
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C.
12.5Ω
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D.
15Ω
Solution
For balance, P/Q = R/S => 10/15 = 5/x => x = 7.5Ω.
Correct Answer: C — 12.5Ω
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Q. If the resistances in a Wheatstone bridge are P = 3Ω, Q = 6Ω, R = 1.5Ω, and S = 3Ω, is the bridge balanced?
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A.
Yes
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B.
No
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C.
Cannot be determined
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D.
Only if P = R
Solution
The bridge is not balanced because P/Q ≠ R/S.
Correct Answer: B — No
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Q. If the resistances in a Wheatstone bridge are R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, and R4 = xΩ, what value of x will balance the bridge?
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A.
7.5Ω
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B.
10Ω
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C.
12.5Ω
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D.
15Ω
Solution
Using the balance condition R1/R2 = R3/R4, we have 10/15 = 5/x, solving gives x = 7.5Ω.
Correct Answer: A — 7.5Ω
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Q. If the resistances in a Wheatstone bridge are R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, and R4 = 7.5Ω, is the bridge balanced?
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A.
Yes
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B.
No
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C.
Depends on the voltage
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D.
Not enough information
Solution
The bridge is balanced if R1/R2 = R3/R4. Here, 10/15 = 5/7.5, which simplifies to 2/3 = 2/3, confirming the bridge is balanced.
Correct Answer: A — Yes
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Q. If the resistances in a Wheatstone bridge are R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, what is the value of R4 for the bridge to be balanced?
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A.
7.5Ω
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B.
10Ω
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C.
12.5Ω
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D.
15Ω
Solution
Using the balance condition R1/R2 = R3/R4, we have 10/15 = 5/R4. Solving gives R4 = 7.5Ω.
Correct Answer: C — 12.5Ω
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Q. If the resistances in a Wheatstone bridge are R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, what should R4 be for the bridge to be balanced?
-
A.
7.5Ω
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B.
10Ω
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C.
12.5Ω
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D.
15Ω
Solution
Using the balance condition R1/R2 = R3/R4, we find R4 = (R2 * R3) / R1 = (15 * 5) / 10 = 7.5Ω.
Correct Answer: C — 12.5Ω
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Q. If the resistances in a Wheatstone bridge are R1 = 10Ω, R2 = 20Ω, R3 = 15Ω, what is the value of R4 for the bridge to be balanced?
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A.
30Ω
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B.
20Ω
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C.
15Ω
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D.
10Ω
Solution
Using the balance condition R1/R2 = R3/R4, we find R4 = (R2 * R3) / R1 = (20 * 15) / 10 = 30Ω.
Correct Answer: B — 20Ω
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Q. If the resistances in a Wheatstone bridge are R1 = 10Ω, R2 = 20Ω, R3 = 15Ω, what should R4 be for the bridge to be balanced?
-
A.
30Ω
-
B.
15Ω
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C.
20Ω
-
D.
10Ω
Solution
Using the balance condition R1/R2 = R3/R4, we find R4 = (R2 * R3) / R1 = (20 * 15) / 10 = 30Ω.
Correct Answer: B — 15Ω
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Q. If the resistances in a Wheatstone bridge are R1 = 20Ω, R2 = 30Ω, and R3 = 10Ω, what is the value of R4 for the bridge to be balanced?
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A.
15Ω
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B.
20Ω
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C.
25Ω
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D.
30Ω
Solution
Using the balance condition R1/R2 = R3/R4, we have 20/30 = 10/x, solving gives x = 20Ω.
Correct Answer: B — 20Ω
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Q. If the resistances in a Wheatstone bridge are R1, R2, R3, and R4, what is the condition for balance?
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A.
R1/R2 = R3/R4
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B.
R1 + R2 = R3 + R4
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C.
R1 * R4 = R2 * R3
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D.
R1 - R2 = R3 - R4
Solution
The condition for balance in a Wheatstone bridge is R1/R2 = R3/R4.
Correct Answer: A — R1/R2 = R3/R4
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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?
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A.
0.09 Ω
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B.
0.18 Ω
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C.
0.27 Ω
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D.
0.36 Ω
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?
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A.
0.12 Ω
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B.
0.15 Ω
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C.
0.18 Ω
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D.
0.20 Ω
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 fixed length and cross-sectional area?
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A.
It doubles
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B.
It halves
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C.
It remains the same
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D.
It quadruples
Solution
Resistance R is directly proportional to resistivity; if resistivity doubles, resistance also doubles.
Correct Answer: A — It doubles
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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?
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A.
It doubles
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B.
It halves
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C.
It remains the same
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D.
It quadruples
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?
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A.
Halved
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B.
Doubled
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C.
Remains the same
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D.
Quadrupled
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?
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A.
Halved
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B.
Doubled
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C.
Remains the same
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D.
Quadrupled
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?
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A.
Halved
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B.
Doubled
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C.
Remains the same
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D.
Quadrupled
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?
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A.
Infinite
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B.
Zero
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C.
Depends on temperature
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D.
Undefined
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?
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A.
0.168 Ω
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B.
0.168 kΩ
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C.
1.68 Ω
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D.
1.68 kΩ
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 supply voltage in a Wheatstone bridge is increased, how does it affect the balance condition?
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A.
It does not affect the balance condition
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B.
It makes the bridge unbalanced
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C.
It increases the current in the circuit
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D.
It decreases the resistance
Solution
Increasing the supply voltage does not affect the balance condition; it remains dependent on the resistance ratios.
Correct Answer: A — It does not affect the balance condition
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Q. If the temperature of a conductor increases, what happens to its resistivity?
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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 material
Solution
For most conductors, resistivity increases with temperature due to increased atomic vibrations.
Correct Answer: A — Increases
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