Question

In a semiconductor, ​if the ratio of the concentration of electrons to that of holes is $\frac{k}{4}$, the ratio of currents is $\frac{5}{4}$ and the ratio of their drift velocities is $\frac{9}{7}$, then the value of $k$ is .

Answer 1

We know that,

$I=n_{e}A{v}_d$

$\Rightarrow \frac{I_e}{I_n}=\frac{n_e\times (v_d{)}_e}{n_h\times (v_d{)}_h}$

Given that,

​​​​​​​$\frac{n_e}{n_h}=\frac{k}{4},\frac{I_e}{I_h}=\frac{9}{4},\frac{(v_d{)}_e}{(v_d{)}_h}=\frac{9}{7}$

$\Rightarrow \frac{9}{4}=\frac{k}{4}\times \frac{9}{7}$

$\therefore k=7$