A) \[0\]
B) \[1/\sqrt{1+{{a}^{2}}}\]
C) \[\sqrt{1+{{a}^{2}}}\]
D) None of these
Correct Answer: B
Solution :
Since, capacitive impedance is a times the resistance in the RC series AC circuit. Therefore, \[{{Z}^{2}}={{R}^{2}}+X_{C}^{2}\] According to the question \[{{X}_{C}}=aR\] Therefore, \[{{Z}^{2}}={{R}^{2}}+{{a}^{2}}{{R}^{2}}\] \[Z=R\sqrt{1+{{a}^{2}}}\] Power factor \[\cos \phi =R/Z=1/\sqrt{1+{{a}^{2}}}\]
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