Chapter Admittance

Teach Yourself Electricity and Electronics Third Edition Book
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Teach Yourself Electricity and Electronics Third Edition Book

  • Remembering that 100 pF 0. 000100 µF, you can substitute in this formula for f3.00 and C0.000100, gettingXC1/(Ωj531The susceptance, BC, is equal to l/XC. Thus, BC1/( j531)j0.00188. Remem-ber that capacitive susceptance is positive. This can “short-circuit” any frustration youmight have in manipulating the minus signs in these calculations.Note that above, you found a reciprocal of a reciprocal. You did something and thenimmediately turned around and undid it, slipping a minus sign in because of the idio-syncrasies of that little j operator. In the future, you can save work by remembering thatthe formula for capacitive susceptance simplified, isBC6.28fC siemensj(6.28fC)This resembles the formula for inductive reactance.Problem 15-6An inductor has L163 µH at a frequency of 887 kHz. What is BL?First, calculate XL, the inductive reactanceXL6.28fL6.280.887163908Ωj908The susceptance, BL is equal to 1/XL Therefore, BL1/j908j0. 00110. Remem-ber that inductive susceptance is negative.The formula for inductive susceptance is similar to that for capacitive reactance:BL 1/(6.28fl) siemens j(1/(6.28fL)AdmittanceConductance and susceptance combine to form admittance, symbolized by the capitalletter Y.Admittance, in an ac circuit, is analogous to conductance in a dc circuit.Complex admittanceAdmittance is a complex quantity and represents the ease with which current can flowin an ac circuit. As the absolute value of impedance gets larger, the absolute value of ad-mittance becomes smaller, in general. Huge impedances correspond to tiny admit-tances, and vice-versa.Admittances are written in complex form just like impedances. But you need tokeep track of which quantity you’re talking about! This will be obvious if you use thesymbol, such as Y3 – j0.5 or Y7j3. When you see Y instead of Z, you know thatnegative j factors (such as –j0.5) mean that there is a net inductance in the circuit, andpositive j factors (such as j3) mean there is net capacitance.276 Impedance and admittance