Magnetic Fields and Electromagnetic Induction

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Q1. If a circuit has a total resistance of 12Ω and a total voltage of 24V, what is the power consumed by the circuit?

Solution:

Power P = V^2 / R = (24V)^2 / 12Ω = 48 W.

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Q2. What is the time constant of an RC circuit with a resistance of 5 kΩ and a capacitance of 10 µF?

Solution:

Time constant τ = R * C = 5000Ω * 10 x 10^-6 F = 0.05 s.

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Q3. In a parallel circuit with two resistors of 6Ω and 12Ω, what is the total resistance?

Solution:

1/R_eq = 1/R1 + 1/R2 = 1/6 + 1/12 = 1/4. Therefore, R_eq = 4Ω.

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Q4. What is the magnetic field strength at a distance of 0.1 m from a long straight wire carrying a current of 5 A?

Solution:

Using the formula B = (μ0 * I) / (2 * π * r), where μ0 = 4π x 10^-7 T m/A, B = (4π x 10^-7 * 5) / (2 * π * 0.1) = 0.01 T.

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Q5. What is the potential difference between two points in an electric field of 500 N/C over a distance of 4 m?

Solution:

V = E * d = 500 N/C * 4 m = 2000 V.

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Q6. What is the equivalent capacitance of two capacitors, 3 µF and 6 µF, connected in series?

Solution:

1/C_eq = 1/C1 + 1/C2 = 1/3 + 1/6 = 1/2. Therefore, C_eq = 2 µF.