The effect of increase in temperature on the number of electrons in conduction band $\left( n _{ e }\right)$ and resistance of a semiconductor will be as:
This phenomenon is observed in semiconductors, where the conductivity significantly improves with temperature. In conductors, however, the increase in temperature typically causes the atoms to vibrate more, which leads to an increase in scattering of the free electrons, thereby increasing the resistance.
The relationship between conductivity and temperature is especially important in devices like thermistors, where the resistance changes significantly with temperature. Positive temperature coefficient (PTC) thermistors show an increase in resistance with temperature, while negative temperature coefficient (NTC) thermistors exhibit the opposite behavior, which makes them useful for temperature sensing and circuit protection applications.
In summary, for most semiconductors, as temperature rises, the number of charge carriers increases, which lowers the resistance, making these materials more conductive. However, in metals and conductors, increased temperature leads to higher resistance due to increased atomic vibrations.
The graph shows the variation of current with voltage for a p-n junction diode. Estimate the dynamic resistance of the diode at \( V = -0.6 \) V.

Let \( a \in \mathbb{R} \) and \( A \) be a matrix of order \( 3 \times 3 \) such that \( \det(A) = -4 \) and \[ A + I = \begin{bmatrix} 1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2 \end{bmatrix} \] where \( I \) is the identity matrix of order \( 3 \times 3 \).
If \( \det\left( (a + 1) \cdot \text{adj}\left( (a - 1) A \right) \right) \) is \( 2^m 3^n \), \( m, n \in \{ 0, 1, 2, \dots, 20 \} \), then \( m + n \) is equal to:
Rate law for a reaction between $A$ and $B$ is given by $\mathrm{R}=\mathrm{k}[\mathrm{A}]^{\mathrm{n}}[\mathrm{B}]^{\mathrm{m}}$. If concentration of A is doubled and concentration of B is halved from their initial value, the ratio of new rate of reaction to the initial rate of reaction $\left(\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}}\right)$ is
Semiconductors are a crystalline solid materials, whose electrical conductivity lies between a conductor and an insulator. Semiconductors are mainly used in the manufacturing of electronic devices like capacitors, transistors, diodes, Integrated circuits, etc.