In a parallel RLC circuit, if R = 50Ω, L = 0.2 H, and C = 50μF, what is the qual

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Question: In a parallel RLC circuit, if R = 50Ω, L = 0.2 H, and C = 50μF, what is the quality factor Q? (2015)

Options:

Correct Answer: 2

Solution:

Quality factor Q = (1/R) * √(L/C) = (1/50) * √(0.2/50e-6) = 2.

In a parallel RLC circuit, if R = 50Ω, L = 0.2 H, and C = 50μF, what is the quality factor Q? (2015)

In a parallel RLC circuit, if R = 50Ω, L = 0.2 H, and C = 50μF, what is the quality factor Q? (2015)

Step 1: Identify the values given in the problem. We have R = 50Ω, L = 0.2 H, and C = 50μF.
Step 2: Convert the capacitance from microfarads to farads. 50μF = 50 * 10^-6 F = 0.00005 F.
Step 3: Write down the formula for the quality factor Q in a parallel RLC circuit: Q = (1/R) * √(L/C).
Step 4: Substitute the values into the formula. Q = (1/50) * √(0.2/0.00005).
Step 5: Calculate the value inside the square root: 0.2 / 0.00005 = 4000.
Step 6: Find the square root of 4000: √4000 = 63.2455532.
Step 7: Now multiply by (1/50): Q = (1/50) * 63.2455532.
Step 8: Calculate (1/50) * 63.2455532 = 1.264911064.
Step 9: Round the result to a reasonable number of significant figures. Q ≈ 2.

Quality Factor in RLC Circuits – The quality factor Q is a dimensionless parameter that describes the damping of the circuit, defined as Q = (1/R) * √(L/C) for parallel RLC circuits.