If $R$ and $L$ represent respectively resistance and self inductance, which of the following combinations has the dimensions of frequency

Heat produced in a current carrying conducting wire depends on current $I$, resistance $R$ of the wire and time $t$ for which current is passed. Using these facts, obtain the formula for heat energy.

In the relation $y = a\cos (\omega t – kx)$, the dimensional formula for $k$ is

A length-scale $(l)$ depends on the permittivity $(\varepsilon)$ of a dielectric material. Boltzmann constant $\left(k_B\right)$, the absolute temperature $(T)$, the number per unit volune $(n)$ of certain charged particles, and the charge $(q)$ carried by each of the particless. Which of the following expression($s$) for $l$ is(are) dimensionally correct?

($A$) $l=\sqrt{\left(\frac{n q^2}{\varepsilon k_B T}\right)}$

($B$) $l=\sqrt{\left(\frac{\varepsilon k_B T}{n q^2}\right)}$

($C$)$l=\sqrt{\left(\frac{q^2}{\varepsilon n^{2 / 3} k_B T}\right)}$

($D$) $l=\sqrt{\left(\frac{q^2}{\varepsilon n^{1 / 3} k_B T}\right)}$