A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 kΩ , an inductor of inductive reactance X L = 250 π Ω and an unknown capacitor. The value of capacitance to max

Question

A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 kΩ , an inductor of inductive reactance X L = 250 π Ω and an unknown capacitor. The value of capacitance to maximise the average power should be: take π 2 = 10

TestHub · Accepted Answer

Angular frequency, ω = 2 π f = 2 π × 50 = 100 π rad s - 1 At resonance, X C = X L ⇒ 1 ωC = ωL ⇒ 1 ωC = 250 π ⇒ C = 1 100 π × 250 π F = 4 μF

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