If R , X L , and X C represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless :

Question

If R , X L , and X C represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless : (A) R XL XC (B) (R/√XL XC) (C) (R/XL XC) (D) R (XL/XC)

Tardigrade Admin · Accepted Answer

All three have same dimension therefore (R/√XL XC) is dimensionless.

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

$R X_{L} X_{C}$

$\frac{R}{X _{L} X _{C}}$

$\frac{R}{X _{L} X _{C}}$

$R \frac{X _{L}}{X _{C}}$

All three have same dimension therefore $\frac{R}{X _{L} X _{C}}$ is dimensionless.

Q. If R,XL​, and XC​ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless :

RXL​XC​

XL​XC​​R​

XL​XC​R​

RXC​XL​​

All three have same dimension therefore XL​XC​​R​ is dimensionless.

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

$R X_{L} X_{C}$

$\frac{R}{X _{L} X _{C}}$

$\frac{R}{X _{L} X _{C}}$

$R \frac{X _{L}}{X _{C}}$

All three have same dimension therefore $\frac{R}{X _{L} X _{C}}$ is dimensionless.