Susceptance:

Sometimes, you will come across term susceptance in reference to an alternating current circuit containing a capacitive reactance or an inductive reactance. Susceptance can be symbolized by B. It is reciprocal of reactance that is, B=1/X. Susceptance can be capacitive or inductive. These are symbolized as B_C and B_L respectively. Thus, B_C =1/X_C, and B_L =1/X_L.

There is a simple trick to determe susceptances in the terms of reactances, or, better stated, trickiness. Susceptance is imaginary and so is reactance. That is, all the values of B are required the use the j operator, just as do all values of X. But 1/j =- j. This reverses sign when you find the susceptance in terms of reactance.

If you have the inductive reactance of 2 ohms, then this can be expressed as j2 in imaginary sense. What is 1/(j2)?  You can break this and say that 1/(j2)=(1/j)(1/2)=(1/j)0.5. But what do you menan by 1/j? Without making this into a mathematical treatise, suffice it to say that 1/j =-j. Thus, the reciprocal of j2 is -j0.5. Inductive susceptance is negative imaginary.

If you have the capacitive reactance XC   10 ohms, then this can be expressed as X_C =j10. The reciprocal of it is B_C =1/( -j10) = (1/-j)(1/10) = (1/-j)0.1. What is1/j? Again, without going into theoretical math, it is equal to j. Thus, the reciprocal of -j10 is j0.1. The Capacitive susceptance is positive imaginary. This is reversed from the situation with reactances.

Problem:

Assume that you have a capacitor of 100 pF at the frequency of 3.00 MHz. What is B_C?

First, find reactance X_C by formula

X_C = -1/(6.28fC)

Keeping in mind that 100 pF = 0. 000100 µF, you can substitute in this formula for f= 3.00 and C =0.000100, we get

X_C =-1/(6.28 *3.00 *0.000100)

= -1/0.001884 = -531O = -j531

The susceptance,  B_C= l/X_C. Therefore, B_C =1/(- j531)   j0.00188. Remember that capacitive susceptance  is positive. This can"short-circuit any frustration you may have in manipulating minus signs in these calculations.

Above, you found a reciprocal of a reciprocal. You did something and then turned around immediately and undid it, slipping the minus sign in due to the idiosyncrasies of that little j operator.  In the future, you can save work by the formula for capacitive susceptance simplified, is

B_C = 6.28fC siemens = j(6.28fC) This resembles formula for the inductive reactance.