# What's the relationship between susceptance and reactance?

I was trying to find the relationship between these two online, but I found out two completely opposite answers, and I'm wondering which one is the right one.

Is B = -1/X or is B = 1/X ?

• I've always seen it as B=1/X, though I'm not confident enough in that to say so definitively. Susceptance doesn't come up very often in my field of study. May 6 '18 at 14:15

Impedance consists of a real part (reistance) and an imaginery part (reactance). Admittance, defined as the reciprocal of impedance, also has a real part (conduction) and an imaginery part (susceptance). If you have a pure reactance, for which the resistance is 0, then the formula reduces to admittance = 1/jX, where X is the reactance. This, in return, simplifies to admittance = -1/X. Thus the answer is that B, the susceptance is equal to -1/X.

Susceptance ($$\B\$$), is a component of Admittance ($$\Y\$$). Admittance ($$\Y\$$) is defined as the current ($$\I\$$) flowing per unit of applied voltage ($$\V\$$). $$\Y= I/V\$$ which is the reciprocal of Impedance ($$\Z\$$), where $$\Z= V/I\$$. Impedance ($$\Z\$$) is a complex number having a real Resistance ($$\R\$$) and an imaginary component Reactance ($$\X\$$), such that $$\Z=R+jX\$$.

But reactance itself is made up of inductive or capacitive components $$\Z=R+j(X_L-X_C)\$$. THIS is where that elusive (-) comes from. So it is that Admittance ($$\Y\$$) is a complex number comprising real Conductance ($$\G\$$) and imaginary Susceptance ($$\B\$$).

$$\Y=G +jB\$$ which in more detail is $$\Y=G+j(B_L-B_C)\$$. Now if there is a pure inductance then $$\G\$$ and $$\B_C\$$ are both zero and $$\Y = jB\$$ if there is a pure capacitance then $$\Y = -jB\$$. The positive and negative indicate whether the admittance relates to pure inductance or capacitance.

• Sorry Y=jB relates to pure capacitive reactance and Y= -JB related to pure inductive reactance. The difference from my previous answer is because I omitted to take the inverse Jan 16 '20 at 16:54
• you can edit the answer Jan 16 '20 at 17:29

Reactance is positive = X (A reactance would be 2000 Ohms not -2000 Ohms)

So susceptance is also positive = 1/X

Capacitor's impedance = -jXC

Inductor's impedance = jXL