If $L$ and $R$ denote inductance and resistance, respectively, then the dimensions of $L/R$ are

We know $E=\dfrac { 1 }{ 2 } L{ i }^{ 2 }\quad \Rightarrow \quad L=\dfrac { 2E }{ { i }^{ 2 } }$

$\Rightarrow$ dimension of $L=\dfrac { { MLT }^{ -2 } }{ { Q }^{ 2 } } .{ T }^{ 2 }={ MLT }^{ 0 }{ Q }^{ -2 }$

Also we know $E={ i }^{ 2 }RT\Rightarrow R=\dfrac { E }{ { i }^{ 2 }t }$

dimension of $R=\dfrac { { MLT }^{ -2 } }{ { Q }^{ 2 } } .{ T }^{ -1 }={ MLT }^{ -1 }{ Q }^{ -2 }$

$\therefore$ $dim\left( \dfrac { L }{ R } \right) =\dfrac { { MLT }^{ 0 }{ Q }^{ -2 } }{ { MLT }^{ -1 }{ Q }^{ -2 } } =\left[ T \right]$