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=(\sqrt{R^2+X^2})^2=R^2+X^2Re-arranging gives:
X^2=Z^2-R^2Taking 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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