S, [I][T]^{-1}

Step 1: Understand the concept of admittance. Admittance, denoted by the symbol Y, is a measure used in electrical engineering that represents how easily a circuit or device will allow a current to flow. It is the inverse of impedance.
Step 2: The unit of admittance (Y) is the Siemens (S).
Step 3: The dimension of admittance can be derived from its relation to current (I) and voltage (V). Since admittance is defined as Y = I/V, using dimensional analysis we find:
- Current (I) has the dimension of [I].
- Voltage (V) has the dimension of [M][L^{2}][T^{-3}][I^{-1}] (from electric potential).
Rearranging the units gives us the dimension of admittance:
$$ [Y] = \frac{[I]}{[M][L^{2}][T^{-3}][I^{-1}]} = [I][M^{-1}][L^{-2}][T^{3}] $$.
This simplifies to:
Therefore, the units and dimensions of admittance are:
Unit: Siemens (S)
Dimension: [I][T]^{-1}.