Question

The admittance of the impedance $\mathbf{-}\mathbf{j}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\Omega }$ is given by

(a) $\mathbf{2}\mathbf{jS}$

(b) $\mathbf{2}{\mathbf{jS}}^{\mathbf{2}}$

(c) $\mathbf{-}\mathbf{4}\mathbf{jS}$

Short answer

Answer

The correct option is (a); that is$2jS$

Step-by-step solution

Define admittance

Consider that impedance is represented by $Z$and admittance is represented by $Y$.

Then, admittance in terms of impedance is as follows:

$\mathbf{Y}\mathbf{=}\frac{\mathbf{1}}{\mathbf{Z}}$ ……. (1)

Use the formula of admittance

Substituting $-j\frac{1}{2}$for$Z$ in Equation (1), we have:

$Y=\frac{1}{Z}$

=$$\begin{gathered} \frac{1}{-j{\displaystyle \frac{1}{2}}} \\ =j2S \end{gathered}$$

Thus, Option (a) is correct.

Explanation for Option (b)

We know from Equation (1) thatadmittance is the inverse of impedance. The unit of admittance is the siemens (S).

Since the unit in Option (b) is the square of siemens, it is incorrect.

Explanation for Option (c)

We know from Equation (1) thatadmittance is the inverse of impedance and the inverse of$-j\frac{1}{2}$ is $j2$ and not $-4js$.

Thus, Option (c) is incorrect.