In a biprism experiment,if the $5^{\text{th}}$ bright band with wavelength $\lambda_{1}$ coincides with the $6^{\text{th}}$ dark band with wavelength $\lambda_{2}$,then the ratio $\left(\frac{\lambda_{2}}{\lambda_{1}}\right)$ is:

$A$ capacitor stores $60 \ \mu C$ charge when connected across a battery. When the gap between the plates is filled with a dielectric,an additional charge of $120 \ \mu C$ flows through the battery. The dielectric constant of the material inserted between the plates of the capacitor is

Consider a block of conducting material of resistivity ' $\rho$ ' shown in the figure. Current ' $I$ ' enters at ' $A$ ' and leaves from ' $D$ '. We apply the superposition principle to find the voltage ' $\Delta V$ ' developed between ' $B$ ' and ' $C$ '. The calculation is done in the following steps:
$(i)$ Take current ' $I$ ' entering from ' $A$ ' and assume it to spread over a hemispherical surface in the block.
(ii) Calculate the field $E(r)$ at distance ' $r$ ' from $A$ by using Ohm's law $E = \rho j$,where $j$ is the current per unit area at ' $r$ '.
(iii) From the ' $r$ ' dependence of $E(r)$,obtain the potential $V(r)$.
(iv) Repeat $(i)$,$(ii)$ and $(iii)$ for current ' $I$ ' leaving ' $D$ ' and superpose results for ' $A$ ' and ' $D$ '.
For current entering at $A$,the electric field at a distance ' $r$ ' from $A$ is

In $\triangle ABC$,$\frac{r_1-r}{a}+\frac{r_2-r}{b}+\frac{r_3-r}{c} =$

The product $(A)$ is:

Which of the following is responsible for the formation of peat?