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If \mathrm{R,X_{L}\: and\: X_{C}}  represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless :

Option: 1

\mathrm{\frac{R}{x_{L}x_{c}}}


Option: 2

\mathrm{\frac{R}{\sqrt{x_{L}x_{c}}}}


Option: 3

\mathrm{R\frac{x_{L}}{x_{c}}}


Option: 4

\mathrm{RX_{L}X_{c}}


Answers (1)

best_answer

\mathrm{R,X_{L},X_{c}} have same unit i.e \mathrm{ohm}

\mathrm{\frac{R}{\sqrt{x_{L}}x_{c}}\rightarrow \frac{ohm}{\sqrt{ohm^{2}}}\rightarrow Dimensionless}

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