Discussion
Find the impedance of an inductive coil having an inductive reactance of 50 Ohms and resistance of 4 Ohms.
Answer: B
The impedance of a coil is the square root of the sum of the squares of the resistance and the reactance, since the two are at right angles in the impedance triangle.
\[ Z = \sqrt{R^{2} + X_{L}^{2}} \]
\[ Z = \sqrt{4^{2} + 50^{2}} = \sqrt{2516} \]
\[ Z \approx 50.16\ \Omega \]
So the impedance is about 50.15 ohms, option (B), which is only a little more than the reactance because the resistance is small. Values of 110.12, 25 and 33 ohms do not follow from the formula.
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