Q. What is the equivalent resistance of a circuit with two resistors R1 = 10Ω and R2 = 10Ω in parallel?
A.
5Ω
B.
10Ω
C.
20Ω
D.
15Ω
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Solution
The equivalent resistance in parallel is given by 1/R_total = 1/R1 + 1/R2 = 1/10 + 1/10 = 1/5. Therefore, R_total = 5Ω.
Correct Answer: A — 5Ω
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Q. What is the equivalent resistance of three resistors of 2 ohms, 3 ohms, and 6 ohms connected in series?
A.
1 ohm
B.
3 ohms
C.
11 ohms
D.
12 ohms
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Solution
In series, the equivalent resistance is the sum of the individual resistances: R_eq = R1 + R2 + R3 = 2 + 3 + 6 = 11 ohms.
Correct Answer: C — 11 ohms
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Q. What is the equivalent resistance of three resistors of 2Ω, 3Ω, and 5Ω connected in parallel?
A.
1Ω
B.
2Ω
C.
0.83Ω
D.
10Ω
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Solution
1/Req = 1/R1 + 1/R2 + 1/R3 = 1/2 + 1/3 + 1/5 = 0.8333, thus Req = 1.2Ω.
Correct Answer: C — 0.83Ω
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Q. What is the equivalent resistance of three resistors of 2Ω, 3Ω, and 6Ω connected in series?
A.
11Ω
B.
10Ω
C.
9Ω
D.
12Ω
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Solution
In series, R_eq = R1 + R2 + R3 = 2 + 3 + 6 = 11Ω.
Correct Answer: A — 11Ω
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Q. What is the equivalent resistance of three resistors of 2Ω, 3Ω, and 6Ω connected in parallel?
A.
1Ω
B.
2Ω
C.
3Ω
D.
4Ω
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Solution
1/R_eq = 1/R1 + 1/R2 + 1/R3 = 1/2 + 1/3 + 1/6 = 1. Therefore, R_eq = 1Ω.
Correct Answer: A — 1Ω
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Q. What is the equivalent resistance of three resistors of values 2Ω, 3Ω, and 5Ω connected in parallel?
A.
1Ω
B.
2Ω
C.
0.83Ω
D.
10Ω
Show solution
Solution
1/R_eq = 1/R1 + 1/R2 + 1/R3 = 1/2 + 1/3 + 1/5 = 0.8333, thus R_eq = 1.2Ω.
Correct Answer: C — 0.83Ω
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Q. What is the equivalent resistance of three resistors of values 2Ω, 3Ω, and 6Ω connected in parallel?
A.
1Ω
B.
2Ω
C.
3Ω
D.
4Ω
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Solution
1/Req = 1/R1 + 1/R2 + 1/R3 = 1/2 + 1/3 + 1/6 = 1. Therefore, Req = 1Ω.
Correct Answer: B — 2Ω
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Q. What is the equivalent resistance of three resistors, 2Ω, 3Ω, and 6Ω, connected in series?
A.
11Ω
B.
6Ω
C.
3Ω
D.
2Ω
Show solution
Solution
In series, the equivalent resistance is the sum of the individual resistances: R_eq = R1 + R2 + R3 = 2Ω + 3Ω + 6Ω = 11Ω.
Correct Answer: A — 11Ω
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Q. What is the equivalent resistance of three resistors, R1, R2, and R3, connected in series?
A.
R1 + R2 + R3
B.
1/(1/R1 + 1/R2 + 1/R3)
C.
R1 * R2 * R3
D.
R1 - R2 - R3
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Solution
In a series connection, the total or equivalent resistance is the sum of the individual resistances.
Correct Answer: A — R1 + R2 + R3
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Q. What is the equivalent resistance of two resistors of 10 ohms and 20 ohms connected in series?
A.
30 ohms
B.
20 ohms
C.
10 ohms
D.
5 ohms
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Solution
In series, the equivalent resistance R_eq = R1 + R2 = 10 ohms + 20 ohms = 30 ohms.
Correct Answer: A — 30 ohms
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Q. What is the equivalent resistance of two resistors of 4Ω and 12Ω connected in parallel?
A.
3Ω
B.
4Ω
C.
6Ω
D.
8Ω
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Solution
Using the formula for parallel resistors, 1/R_eq = 1/R1 + 1/R2 = 1/4 + 1/12 = 1/3. Therefore, R_eq = 3Ω.
Correct Answer: C — 6Ω
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Q. What is the equivalent resistance of two resistors of 5 ohms and 10 ohms connected in parallel?
A.
3.33 ohms
B.
15 ohms
C.
5 ohms
D.
7.5 ohms
Show solution
Solution
Using the formula for resistors in parallel, 1/R_eq = 1/R1 + 1/R2, we find R_eq = 1 / (1/5 + 1/10) = 3.33 ohms.
Correct Answer: A — 3.33 ohms
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Q. What is the equivalent resistance of two resistors of 5Ω and 10Ω connected in parallel?
A.
3.33Ω
B.
5Ω
C.
7.5Ω
D.
15Ω
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Solution
1/Req = 1/R1 + 1/R2 = 1/5 + 1/10 = 2/10 + 1/10 = 3/10. Therefore, Req = 10/3 = 3.33Ω.
Correct Answer: A — 3.33Ω
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Q. What is the equivalent resistance of two resistors, 6 ohms and 3 ohms, connected in series?
A.
2 ohms
B.
3 ohms
C.
9 ohms
D.
18 ohms
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Solution
In series, the equivalent resistance is the sum: R_eq = R1 + R2 = 6Ω + 3Ω = 9Ω.
Correct Answer: C — 9 ohms
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Q. What is the equivalent resistance of two resistors, 6Ω and 3Ω, connected in series?
A.
2Ω
B.
3Ω
C.
9Ω
D.
18Ω
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Solution
In series, the equivalent resistance (R_eq) is the sum of the resistances: R_eq = 6Ω + 3Ω = 9Ω.
Correct Answer: C — 9Ω
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Q. What is the escape velocity for a satellite to leave Earth's gravitational field?
A.
7.9 km/s
B.
11.2 km/s
C.
9.8 km/s
D.
5.0 km/s
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Solution
The escape velocity from the Earth's surface is approximately 11.2 km/s.
Correct Answer: B — 11.2 km/s
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Q. What is the escape velocity for a satellite to leave the Earth's gravitational field?
A.
7.9 km/s
B.
11.2 km/s
C.
9.8 km/s
D.
5.0 km/s
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Solution
The escape velocity from the Earth's surface is approximately 11.2 km/s.
Correct Answer: B — 11.2 km/s
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Q. What is the escape velocity for a satellite to leave the Earth's gravitational influence?
A.
11.2 km/s
B.
7.9 km/s
C.
9.8 km/s
D.
15.0 km/s
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Solution
The escape velocity from the Earth's surface is approximately 11.2 km/s.
Correct Answer: A — 11.2 km/s
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Q. What is the escape velocity from the surface of a planet with a radius of 3R and mass 4M?
A.
√(8GM/R)
B.
√(6GM/R)
C.
√(4GM/R)
D.
√(10GM/R)
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Solution
Escape velocity v = √(2GM/R); here, v = √(2 * 4GM / 3R) = √(8GM/3R).
Correct Answer: A — √(8GM/R)
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Q. What is the escape velocity from the surface of a planet with a radius of 4R and mass 2M?
A.
2√(GM/R)
B.
√(8GM/R)
C.
√(2GM/R)
D.
4√(GM/R)
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Solution
Escape velocity v = √(2GM/R) = √(2 * 2M / 4R) = √(8GM/4R) = √(8GM/R)
Correct Answer: B — √(8GM/R)
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Q. What is the escape velocity from the surface of a planet with mass M and radius R?
A.
√(2GM/R)
B.
√(GM/R)
C.
√(2R/G)
D.
√(G/R)
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Solution
Escape velocity is given by v = √(2GM/R).
Correct Answer: A — √(2GM/R)
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Q. What is the escape velocity from the surface of the Earth?
A.
7.9 km/s
B.
11.2 km/s
C.
9.8 km/s
D.
15 km/s
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Solution
The escape velocity from the surface of the Earth is approximately 11.2 km/s.
Correct Answer: B — 11.2 km/s
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Q. What is the escape velocity from the surface of the Earth? (g = 9.8 m/s^2, R = 6.4 x 10^6 m)
A.
7.9 km/s
B.
11.2 km/s
C.
9.8 km/s
D.
5.0 km/s
Show solution
Solution
Escape velocity (v) = sqrt(2gR) = sqrt(2 * 9.8 * 6.4 x 10^6) ≈ 11.2 km/s.
Correct Answer: B — 11.2 km/s
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Q. What is the expression for the magnetic field at the center of a circular loop of radius R carrying current I?
A.
μ₀I/(2R)
B.
μ₀I/(4R)
C.
μ₀I/(2πR)
D.
μ₀I/(4πR)
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Solution
The magnetic field at the center of a circular loop is given by B = μ₀I/(2R).
Correct Answer: C — μ₀I/(2πR)
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Q. What is the expression for the magnetic field at the center of a circular loop of radius R carrying a current I?
A.
B = μ₀I/(2R)
B.
B = μ₀I/(4R)
C.
B = μ₀I/(πR)
D.
B = μ₀I/(2πR)
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Solution
The magnetic field at the center of a circular loop of radius R carrying a current I is given by B = μ₀I/(2πR).
Correct Answer: D — B = μ₀I/(2πR)
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Q. What is the expression for the magnetic field B at a distance r from a long straight wire carrying current I according to the Biot-Savart Law?
A.
B = (μ₀I)/(2πr)
B.
B = (μ₀I)/(4πr²)
C.
B = (I)/(2Ï€r)
D.
B = (μ₀I²)/(2πr)
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Solution
The magnetic field B at a distance r from a long straight wire carrying current I is given by B = (μ₀I)/(2πr).
Correct Answer: A — B = (μ₀I)/(2πr)
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Q. What is the expression for the magnetic field B at a distance r from a long straight conductor carrying current I?
A.
B = (μ₀I)/(2πr)
B.
B = (μ₀I)/(4πr²)
C.
B = (I)/(2Ï€r)
D.
B = (μ₀I²)/(2πr)
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Solution
The magnetic field B at a distance r from a long straight conductor carrying current I is given by B = (μ₀I)/(2πr).
Correct Answer: A — B = (μ₀I)/(2πr)
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Q. What is the final temperature when 200 g of water at 90°C is mixed with 300 g of water at 30°C?
A.
50°C
B.
60°C
C.
70°C
D.
80°C
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Solution
Using the formula m1*T1 + m2*T2 = (m1 + m2)*Tf, we find Tf = (200*90 + 300*30) / (200 + 300) = 70°C.
Correct Answer: C — 70°C
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Q. What is the first law of thermodynamics?
A.
Energy cannot be created or destroyed
B.
Entropy of an isolated system always increases
C.
Heat cannot spontaneously flow from a colder body to a hotter body
D.
The total energy of a system is constant
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Solution
The first law of thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another.
Correct Answer: A — Energy cannot be created or destroyed
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Q. What is the focal length of a concave lens if it forms a virtual image at a distance of 20 cm from the lens?
A.
-10 cm
B.
-20 cm
C.
10 cm
D.
20 cm
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Solution
For a concave lens, the focal length (f) is negative. The virtual image distance (v) is -20 cm. Using the lens formula 1/f = 1/v + 1/u, we can find f. Since v = -20 cm, we can assume u is at infinity, thus 1/f = 1/(-20) + 0, giving f = -20 cm.
Correct Answer: B — -20 cm
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