Question

A two-port network is defined by the relation 
\(\text{I}_1 = 5V_1 + 3V_2 \)
\(\text{I}_2 = 2V_1 - 7V_2 \)
The value of \( Z_{12} \) is:

• A. 3 ohms
• B. -3 ohms
• C. \(\frac{3}{41}\) ohms
• D. \(\frac{2}{31}\) ohms

Hint:

To find the value of \( Z_{12} \), use the relationship between the voltage and current matrices of the two-port network. \( Z_{12} \) is the coefficient that relates the change in \( V_2 \) to the change in \( I_1 \).

Answer 1

The Correct Option is C

The given relations for the two-port network are:
\[ I_1 = 5V_1 + 3V_2 \] \[ I_2 = 2V_1 - 7V_2 \] To find \( Z_{12} \), we need to use the formula: \[ Z_{12} = \frac{\partial V_2}{\partial I_1} \] From the given equations, we can express the two-port network as a matrix relation: \[ \begin{pmatrix} I_1
I_2 \end{pmatrix} = \begin{pmatrix} 5 & 3
2 & -7 \end{pmatrix} \begin{pmatrix} V_1
V_2 \end{pmatrix} \] From this, the value of \( Z_{12} \) can be calculated as: \[ Z_{12} = \frac{3}{41} \, \text{ohms} \] Thus, the value of \( Z_{12} \) is \( \frac{3}{41} \) ohms.