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?
-
A.
7.5Ω
-
B.
10Ω
-
C.
12.5Ω
-
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?
-
A.
Zero
-
B.
Maximum
-
C.
Minimum
-
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?
-
A.
Zero
-
B.
Equal to the supply voltage
-
C.
Half of the supply voltage
-
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?
-
A.
7.5Ω
-
B.
10Ω
-
C.
12.5Ω
-
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?
-
A.
Yes
-
B.
No
-
C.
Cannot be determined
-
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?
-
A.
7.5Ω
-
B.
10Ω
-
C.
12.5Ω
-
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?
-
A.
Yes
-
B.
No
-
C.
Depends on the voltage
-
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 should R4 be for the bridge to be balanced?
-
A.
7.5Ω
-
B.
10Ω
-
C.
12.5Ω
-
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 = 15Ω, R3 = 5Ω, what is the value of R4 for the bridge to be balanced?
-
A.
7.5Ω
-
B.
10Ω
-
C.
12.5Ω
-
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 = 20Ω, R3 = 15Ω, what is the value of R4 for the bridge to be balanced?
-
A.
30Ω
-
B.
20Ω
-
C.
15Ω
-
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
-
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?
-
A.
15Ω
-
B.
20Ω
-
C.
25Ω
-
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?
-
A.
R1/R2 = R3/R4
-
B.
R1 + R2 = R3 + R4
-
C.
R1 * R4 = R2 * R3
-
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?
-
A.
0.09 Ω
-
B.
0.18 Ω
-
C.
0.27 Ω
-
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?
-
A.
0.12 Ω
-
B.
0.15 Ω
-
C.
0.18 Ω
-
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?
-
A.
It doubles
-
B.
It halves
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C.
It remains the same
-
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?
-
A.
It doubles
-
B.
It halves
-
C.
It remains the same
-
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?
-
A.
Halved
-
B.
Doubled
-
C.
Remains the same
-
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?
-
A.
Halved
-
B.
Doubled
-
C.
Remains the same
-
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?
-
A.
Halved
-
B.
Doubled
-
C.
Remains the same
-
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?
-
A.
Infinite
-
B.
Zero
-
C.
Depends on temperature
-
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?
-
A.
0.168 Ω
-
B.
0.168 kΩ
-
C.
1.68 Ω
-
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 revenue function is R(x) = 100x - 2x^2, find the number of units that maximizes revenue. (2021)
Solution
Max revenue occurs at x = -b/(2a) = 100/(2*2) = 25.
Correct Answer: B — 50
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Q. If the revenue function is R(x) = 20x - 0.5x^2, find the quantity that maximizes revenue. (2021)
Solution
R'(x) = 20 - x = 0 gives x = 20. This maximizes revenue.
Correct Answer: B — 20
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Q. If the revenue function is R(x) = 50x - 0.5x^2, find the number of units that maximizes revenue. (2023)
Solution
Max revenue occurs at x = -b/(2a) = -50/(2*-0.5) = 50.
Correct Answer: A — 25
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Q. If the RMS speed of a gas is 250 m/s, what is the temperature if the molar mass is 0.028 kg/mol?
-
A.
100 K
-
B.
200 K
-
C.
300 K
-
D.
400 K
Solution
Using v_rms = sqrt(3RT/M), we can rearrange to find T = (v_rms^2 * M) / (3R) = 300 K.
Correct Answer: C — 300 K
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Q. If the RMS speed of a gas is 300 m/s and its molar mass is 28 g/mol, what is the temperature of the gas?
-
A.
300 K
-
B.
600 K
-
C.
900 K
-
D.
1200 K
Solution
Using the formula v_rms = sqrt((3RT)/M), we can rearrange to find T = (v_rms^2 * M)/(3R). Plugging in the values gives T = 600 K.
Correct Answer: B — 600 K
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Q. If the RMS speed of a gas is 300 m/s at 300 K, what will be its RMS speed at 600 K?
-
A.
300 m/s
-
B.
600 m/s
-
C.
300√2 m/s
-
D.
600√2 m/s
Solution
The RMS speed is proportional to the square root of the temperature. Therefore, at 600 K, the RMS speed will be 300 * sqrt(2) m/s.
Correct Answer: C — 300√2 m/s
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Q. If the RMS speed of a gas is 300 m/s at 400 K, what will be the RMS speed at 200 K?
-
A.
150 m/s
-
B.
300 m/s
-
C.
600 m/s
-
D.
100 m/s
Solution
The RMS speed is proportional to the square root of the temperature. Therefore, at 200 K, the RMS speed will be 300 * sqrt(200/400) = 150 m/s.
Correct Answer: A — 150 m/s
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Q. If the RMS speed of a gas is 300 m/s at 400 K, what will be the RMS speed at 800 K?
-
A.
300 m/s
-
B.
600 m/s
-
C.
424 m/s
-
D.
848 m/s
Solution
RMS speed is proportional to the square root of temperature. v_rms at 800 K = 300 * sqrt(800/400) = 300 * sqrt(2) = 600 m/s.
Correct Answer: B — 600 m/s
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