If the power factor changes from 0.5 to 0.25 because impedance changes from Z₁ to Z₂ then Z₁=x Z₂ . The value of x is (Resistance remains constant)

Step-by-step solution

The power factor cos φ relates resistance R to impedance Z through = R Z , which rearranges to Z = R . Given ₁ = 0.5 and ₂ = 0.25 with constant resistance, the impedances are Z₁ = R 0.5 and Z₂ = R 0.25 . Substituting Z₁ = xZ₂ yields R 0.5 = x ( R 0.25 ) . Canceling R and simplifying gives x = 0.25 0.5 = 0.5 . The final answer is B .