Chapter 14, Problem 1RQ

To determine

Choose the correct option to find a zero of the transfer function.

Answer to Problem 1RQ

The correct option from the given choices is $\left(\text{b}\right)-1$.

Explanation of Solution

Given data:

The transfer function of a network is,

$H\left(s\right)=\frac{10\left(s+1\right)}{\left(s+2\right)\left(s+3\right)}$ (1)

Formula used:

Write a general form of transfer function.

$H\left(s\right)=\frac{\left(s-z_1\right)\left(s-z_2\right)\left(s-z_3\right)\mathrm{...}\left(s-z_N\right)}{\left(s-p_1\right)\left(s-p_2\right)\left(s-p_3\right)\mathrm{...}\left(s-p_N\right)}$ (2)

Here,

$z_1,z_2,\mathrm{...}{z}_N$ are the number of zeroes, and

$p_1,p_2,\mathrm{...}{p}_N$ are the number of poles.

Calculation:

The equation (1) is written as follows,

$H\left(s\right)=\frac{10\left(s-\left(-1\right)\right)}{\left(s-\left(-2\right)\right)\left(s-\left(-3\right)\right)}$ . (3)

Comparing equation (2) and (3),

$\begin{array}{l}{z}_1=-1\\ p_1=-2\\ p_2=-3\end{array}$

The transfer function has one zero and two poles. The value of the zero is $-1$.

The option (b) is correct and the options (a), (c) and (d) is incorrect.

Conclusion:

Thus, the correct option from the given choices is $\left(\text{b}\right)-1$.