The power factor of an L-R series circuit is 0.6 and that of a C-R series circuit is 0.5. If the elements of the two circuits are joined in series and the resulting power factor is 1, the ratio of the resistance in the L-R circuit to that in the C-R circuit is:
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Question

The power factor of an L-R series circuit is 0.6 and that of a C-R series circuit is 0.5. If the elements of the two circuits are joined in series and the resulting power factor is 1, the ratio of the resistance in the L-R circuit to that in the C-R circuit is:

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G1 Physics · Accepted Answer

Use Z=√[R²+(Xₗ−X꜀)²], Xₗ=ωL, X꜀=1/(ωC), and P̄=VᵣₘₛIᵣₘₛcosφ with cosφ=R/Z. Substitution gives 3ξ 3 4.