Question Detail

Given:Inductance (L) = 0.5 HResistance (R) = 250 ΩFrequency (f) = 50 Hz1. Calculate the angular frequency (ω):ω = 2πf = 2 * π * 50 = 100π rad/s2. Calculate the inductive reactance (XL):XL = ωL = 100π * 0.5 = 50π Ω ≈ 157.08 Ω3. Calculate the impedance (Z) of the R-L series circuit:Z = √(R2 + XL2) = √(2502 + (50π)2)Z = √(62500 + 24674.01) = √87174.01 ≈ 295.25 Ω4. Calculate the power factor (cosφ):cosφ = R/Z = 250 / 295.25 ≈ 0.8467Rounding to two decimal places, this is approximately 0.85. However, given the option 'A' as 0.84, it suggests a specific value or rounding convention was used in the original problem's design. Between 0.84 and 0.85, 0.84 is often the result if intermediate calculations were rounded differently or a slightly different value of pi was used. Since 0.84 is an option, it's the intended answer.