Final answer:
To find the inductive reactance in a parallel RL circuit with a known equivalent impedance, the formula for total impedance in a parallel circuit is used and rearranged. After substituting the given values into this formula, we find that the inductive reactance is not matching any of the provided options, suggesting an error in the question.
Step-by-step explanation:
The subject of the question is Physics, specifically dealing with the impedance in RL and RLC circuits. The question asked pertains to the High School level. The student is trying to find the inductive reactance of the circuit when a 512Ω resistor is connected in parallel to an inductor and the equivalent impedance is given as 412Ω. To solve this problem, we can use the formula for the total impedance of a parallel RL circuit:
Ztotal = Rparallel = (R * XL) / sqrt(R2 + XL2)
Where Ztotal is the total impedance, R is the resistance, and XL is the inductive reactance. We can solve for XL since we have the values for Ztotal and R.
Rearranging the formula to solve for XL gives us:
XL = sqrt((R2 * Ztotal2) / (R2 - Ztotal2))
Substituting the known values:
XL = sqrt((5122 * 4122) / (5122 - 4122))
Calculating this gives an inductive reactance XL = 672.2Ω. None of the given options (a) 4.6722, (b) 6.6702, (c) 8.6722, (d) 10.6722 matches the calculated value, indicating a possible error in the question's options or the student's initial values.