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the percentage increase in the impedence of an ac circuit, when its powerfacor changes from 0.866 to 0.5 is (resistance constant)

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The percentage increase in the impedence can be calculated as: 

cos\phi_1=0.866=\frac{R}{Z_1}\Rightarrow Z_1=1.154R\\ Cos\phi_2=\frac{R}{Z_2}=0.5\Rightarrow Z_2=2R\\PERCRNTAGE\ CHANGE=\frac{2R-1.154R}{1.154R}\times100=73.2

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