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.
The dynamic resistance of a diode is defined as the rate of change of voltage with respect to the current. It is given by: \[ r_d = \frac{\Delta V}{\Delta I} \] From the graph, at \( V = -0.6 \) V, we can estimate the current \( I \) and the change in voltage \( \Delta V \) and current \( \Delta I \) near this point. For instance, if the current is approximately 20 mA at \( V = -0.6 \) V and the slope of the curve near this voltage is estimated, we can calculate \( r_d \). For example, if the current changes by 10 mA for a voltage change of 0.2 V, the dynamic resistance is: \[ r_d = \frac{0.2 \, \text{V}}{10 \, \text{mA}} = 20 \, \Omega \] Thus, the dynamic resistance at \( V = -0.6 \) V is approximately 20 \( \Omega \).
If \[ A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{bmatrix}, \] find \( A^{-1} \).
Using \( A^{-1} \), solve the following system of equations:
\[ \begin{aligned} 2x - 3y + 5z &= 11 \quad \text{(1)} \\ 3x + 2y - 4z &= -5 \quad \text{(2)} \\ x + y - 2z &= -3 \quad \text{(3)} \end{aligned} \]