Question 24: AC fundamentals

Question

If $R$ and $L$ denote resistance and inductance of a material, then the dimension of $L R$ will be:

Accepted Answer

Resistance $R$ (ohm) has the same dimension as voltage/current. Since
Ã¢ÂÂ Voltage $V$ is work per charge: $[V]=M\,L^2\,T^{-3}\,A^{-1}$
Ã¢ÂÂ Resistance $R=V/I$
we get
$      [R]=M\,L^2\,T^{-3}\,A^{-2}.    $
Inductance $L$ (henry) follows from energy in an inductor, $E=	frac12LI^2$, so
$      [L]=\frac{E}{I^2}          =\frac{M\,L^2\,T^{-2}}{A^2}          =M\,L^2\,T^{-2}\,A^{-2}.    $
Multiply them:
$      [L\,R]      =\bigl(M\,L^2\,T^{-2}\,A^{-2}\bigr)        	imes\bigl(M\,L^2\,T^{-3}\,A^{-2}\bigr)      =M^2\,L^4\,T^{-5}\,A^{-4}.    $
That matches Option A.

Answer

$M^2 L^4 T^{-5} A^{-4}$

Answer

$M L T A^{-1}$

Answer

$M^0 L^0 T^0 A^0$

Answer

$M^{-1} L^4 T A^{-3}$

AC fundamentals

If R and L denote resistance and inductance of a material, then the dimension of L R will be:

Choose the correct answer: