A 100 V, AC source of frequency 500 Hz is connected to an LCR circuit with L=8.1 mH, C=12.5 μF, R=10 Ω all connected in series as shown in figure. What is the quality factor of circuit?
Question
A 100 V, AC source of frequency 500 Hz is connected to an LCR circuit with L=8.1 mH, C=12.5 μF, R=10 Ω all connected in series as shown in figure. What is the quality factor of circuit?
Solution
The quality factor (Q) of an LCR circuit is given by the formula:
Q = 1/R * sqrt(L/C)
where: L is the inductance, C is the capacitance, and R is the resistance.
Given that L = 8.1 mH = 8.1 x 10^-3 H, C = 12.5 μF = 12.5 x 10^-6 F, and R = 10 Ω, we can substitute these values into the formula:
Q = 1/10 * sqrt((8.1 x 10^-3)/(12.5 x 10^-6))
Solving the equation gives:
Q = sqrt(0.648) = 0.805
Therefore, the quality factor of the circuit is approximately 0.805.
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