91Ó°ÊÓ

The number of electrons passes through the single thick filament bulb $\mathrm{n}=3×10$¹⁸.

The number of electrons pass through the single thin filament bulb, $\mathrm{n}\text{'}=1.5×10$¹⁸.

The relation between the number of electrons of a thin filament bulb and a combination of thin and thick filament bulb is given as follows,

$\frac{\mathbf{N}}{\mathbf{n}}\mathbf{=}{\frac{\mathbf{R}}{\mathbf{R}}}_{\mathbf{eq}}$ ....(i)

Here, $\mathbf{R}$is the resistance of the thick filament bulb, ${\mathbf{R}}_{\mathbf{eq}}$is the equivalent resistance of the circuit, and$\mathbf{N}$ is the number of the electron passes through the thin filament bulb.

The number of electrons passes through the filament bulb is inversely proportional to the filament bulb.

Calculate the resistance of the single thin filament bulb.

$\mathrm{R}\text{'}=\frac{\mathrm{n}}{\mathrm{n}\text{'}}\mathrm{R}$

Substitute$3×10$¹⁸ for n and $1.5×10$¹⁸ for into the above equation.

$$\begin{gathered} \mathrm{R}\text{'}=\frac{3×{10}^{18}}{1.5×{10}^{18}}\mathrm{R} \\ \mathrm{R}\text{'}=\frac{3}{1.5}\mathrm{R} \\ \mathrm{R}\text{'}=2\mathrm{R} \end{gathered}$$

The equivalent resistance of the given circuit can be calculated as,

$$\begin{gathered} {\mathrm{R}}_{\mathrm{eq}}=\mathrm{R}\text{'}+\frac{\mathrm{R}×\mathrm{R}}{\mathrm{R}+\mathrm{R}} \\ {\mathrm{R}}_{\mathrm{eq}}=\mathrm{R}\text{'}+\frac{\mathrm{R}}{2} \end{gathered}$$

Substitute for into above equation.

$$\begin{gathered} {\mathrm{R}}_{\mathrm{eq}}=2\mathrm{R}+\frac{\mathrm{R}}{2} \\ {\mathrm{R}}_{\mathrm{eq}}=\frac{5}{2}\mathrm{R} \\ {\mathrm{R}}_{\mathrm{eq}}=2.5\mathrm{R} \end{gathered}$$

Calculate the number of electrons passing through the thin filament bulb.

Substitute, localid="1668665406979" $2.5\mathrm{R}$for ${\mathrm{R}}_{\mathrm{eq}}$and $3×10$¹⁸ for n into equation (i).

$$\begin{gathered} \frac{\mathrm{N}}{3×{10}^{18}}=\frac{\mathrm{R}}{2.5\mathrm{R}} \\ \frac{\mathrm{N}}{3×{10}^{18}}=\frac{1}{2.5} \\ \mathrm{N}=\frac{3×{10}^{18}}{2.5} \\ \mathrm{N}=1.2×{10}^{18} \end{gathered}$$

Hence the number of the electron passes through the thin filament bulb is

$1.2×{10}^{18}$