Formula & Calculator
Admittance
The reciprocal of impedance, representing how easily a circuit allows current to flow under AC excitation.
Interpretation
Admittance Y = 1/Z is the reciprocal of impedance, expressed in siemens (S).
It is particularly useful for parallel circuit analysis because admittances add directly.
Example: Z = 4 + j3Ω → Y = 1/(4+j3) = (4−j3)/(16+9) = 0.16 − j0.12 S.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Y | Admittance = 1 / Z | S |
| Z | Impedance = R + jX | Ω |
| G | Conductance = Re(Y) | S |
| B | Susceptance = Im(Y) | S |
What it means
Admittance Y is the reciprocal of impedance Z, defined as Y = 1/Z. It is measured in siemens (S). Admittance is particularly useful for parallel circuit analysis because admittances add directly. The real part of Y is conductance (G), and the imaginary part is susceptance (B). For a resistor, Y = 1/R (G). For an inductor, Y = 1/(jωL) = −j/(ωL). For a capacitor, Y = jωC. Admittance simplifies the calculation of total current in parallel branches, analogous to conductance in DC. Example: If Z = 4 + j3 Ω, then Y = 1/(4+j3) = (4−j3)/(4²+3²) = (4−j3)/25 = 0.16 − j0.12 S. The conductance is 0.16 S, and the susceptance is −0.12 S (capacitive).
Worked example
Admittance – Practical Example
Real‑World| Parameter | Value |
|---|---|
| Z | 4 − j3 Ω |
| Formula | Y = 1 / Z |
Common mistakes
- Admittance: Y = 1/Z – the reciprocal of impedance.
- Units: Siemens (S).
- Conductance G and susceptance B: Y = G + jB – where G = R/(R²+X²), B = −X/(R²+X²).
- Parallel circuits: Admittances add directly (unlike impedances).
- Imaginary part: B positive for capacitive circuits, negative for inductive.
Applications
Admittance Y = 1/Z is the reciprocal of impedance, expressed in siemens. It is particularly useful for parallel circuit analysis, as admittances add directly. Engineers use it to simplify the analysis of parallel circuits, to design parallel resonant circuits, and to calculate branch currents. By using admittance, they can apply Kirchhoff's current law in the frequency domain more conveniently. This concept is also used in network synthesis and filter design. Understanding admittance complements impedance and provides flexibility in solving AC circuits.
- Parallel AC circuit analysis (admittance summation)
- Design of parallel resonant and filter circuits
- Network synthesis and simulation
- Power system analysis (bus admittance matrix)
- Educational understanding of admittance concept
Frequently Asked Questions
Admittance is the reciprocal of impedance: Y = 1 / Z. It represents how easily a circuit allows current to flow under AC excitation. Its unit is siemens (S).
Y = G + jB, where G is conductance (real part) and B is susceptance (imaginary part). Z = R + jX, and Y = (R − jX)/(R²+X²).
Resistor: Y_R = 1/R (pure conductance). Inductor: Y_L = 1/(jωL) = −j/(ωL) (negative susceptance). Capacitor: Y_C = jωC (positive susceptance).
Parallel: Y_total = ΣY_i. Series: 1/Y_total = Σ 1/Y_i (which is the same as adding impedances in series).
In parallel circuits, admittances add directly, making it easier to compute total current from voltage: I = V·Y_total.
Yes, for DC, Y = 1/R (since X_L=0, X_C=∞). The concept is the same but simpler.
The angle of Y is the negative of the impedance angle. The power factor is cos(θ) where θ is the angle of Z (or Y).
Used in circuit analysis, especially for parallel networks, power system load flow, and admittance matrix formulation.
Common errors include: 1) confusing G and B with R and X, 2) using the reciprocal incorrectly, 3) applying admittance in series incorrectly, 4) forgetting the j sign, and 5) using the wrong units.