Question A8.11: The impedance of the a.c. circuit shown in Fig. A8.5 is give...
The impedance of the a.c. circuit shown in Fig. A8.5 is given by:
Z=\sqrt{R^{2}+X^{2}}Determine the reactance, X, of the circuit when R = 25 Ω and Z = 50 Ω.
Here we know that:
R = 25 Ω
Z = 50 Ω
X = ?
First we will re-arrange the formula in order to make X the subject:
Squaring both sides gives:
Z^{2}=\left(\sqrt{R^{2}+X^{2}}\right)^{2}=R^{2}+X^{2}Re-arranging gives:
X^{2}=Z^{2}-R^{2}Taking the square root of both sides gives:
X=\sqrt{Z^{2}-R^{2}}We can now replace Z and R by the values that we know:
X=\sqrt{50^{2}-25^{2}}=\sqrt{2,500-625}=\sqrt{1,875}thus X = 43.3 Ω
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