Given that at a certain frequency, the following circuit has an equivalent impedance magnitude of 428 Ohms and an equivalent resistance of 424 Ohms, what is the magnitude of the reactance?
Question
Given that at a certain frequency, the following circuit has an equivalent impedance magnitude of 428 Ohms and an equivalent resistance of 424 Ohms, what is the magnitude of the reactance?
Solution
The impedance (Z) of a circuit is given by the formula Z = sqrt(R^2 + X^2), where R is the resistance and X is the reactance.
Given that Z = 428 Ohms and R = 424 Ohms, we can rearrange the formula to solve for X:
X = sqrt(Z^2 - R^2)
Substituting the given values:
X = sqrt((428 Ohms)^2 - (424 Ohms)^2)
X = sqrt(183184 Ohms^2 - 179776 Ohms^2)
X = sqrt(3408 Ohms^2)
X = 58.4 Ohms
So, the magnitude of the reactance is 58.4 Ohms.
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