The power factor of an L-R series circuit is 0 . 5 and that of a C-R series circuit is 0 . 2 . If the elements ( L , C a n d R ) of the two circuits are joined in series and connected to the same ac s

Question

The power factor of an L-R series circuit is 0 . 5 and that of a C-R series circuit is 0 . 2 . If the elements ( L , C a n d R ) of the two circuits are joined in series and connected to the same ac source, the power factor of this circuit is found to be 1 . The ratio of the resistance in the L-R circuit to the resistance in the C-R circuit is

TestHub · Accepted Answer

R 1 X L 2 + R 1 2 = 0.5 2 R 1 2 = R 1 2 + X L 2 3 R 1 2 = X L 2 .....(i) R 2 X C 2 + R 2 2 = 0.2 25 R 2 2 = X C 2 + R 2 2 24 R 2 2 = X C 2 = X L 2 (Since the LCR circuit is in resonance, the capacitive reactance and the inductive reactance are equal) 3 R 1 2 = 24 R L 2 R 1 R 2 = 2 2

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