Question E5B06:
What is susceptance?  

Choices:  
A: The magnetic impedance of a circuit  
B: The ratio of magnetic field to electric field  
C: The imaginary part of admittance  
D: A measure of the efficiency of a transformer    

Correct Answer is  C: The imaginary part of admittance  

Correct answer: C — The imaginary part of admittance

1) Why C is correct
- Admittance is the inverse of impedance. In rectangular form:
  $$Y = G + jB$$
  where:
  - $G$ = conductance (real part, in siemens)
  - $B$ = susceptance (imaginary part, in siemens)
- Therefore, susceptance is the imaginary part of admittance.

2) Why the other choices are incorrect
- A: “Magnetic impedance” is not a standard circuit quantity; susceptance is not related specifically to magnetism and is measured in siemens, not ohms.
- B: The ratio of magnetic field to electric field is related to a medium’s intrinsic impedance:
  $$\eta = \sqrt{\mu/\epsilon} \quad \text{(actually } E/H \text{)}$$
  This is not susceptance.
- D: Transformer efficiency involves power losses and coupling, not susceptance.

3) Useful formulas and rules of thumb
- Definitions:
  $$Z = R + jX \quad\Rightarrow\quad Y = \frac{1}{Z} = G + jB$$
  $$Y = \frac{1}{R + jX} = \frac{R - jX}{R^2 + X^2} \Rightarrow 
  G = \frac{R}{R^2 + X^2},\; B = \frac{-X}{R^2 + X^2}$$
- Pure reactances:
  - Inductor: $Z_L = j\omega L \Rightarrow Y_L = -\,\dfrac{j}{\omega L} \Rightarrow B_L = -\,\dfrac{1}{\omega L}$
  - Capacitor: $Z_C = \dfrac{1}{j\omega C} \Rightarrow Y_C = j\omega C \Rightarrow B_C = \omega C$
- Rule of thumb:
  - Capacitive susceptance is positive ($B>0$).
  - Inductive susceptance is negative ($B<0$).
- In parallel networks, admittances (and thus susceptances) add:
  $$B_{\text{total}} = \sum B_i$$