Question

The phase voltage and current across a load element are 100.0 ∠45° V and 5.0 ∠15° A. respectively. Determine the impedance and admittance of the load.
1. Z = 20.0 ∠-30° Ω and Y = 0.05 ∠30° S
2. Z = 20.0 ∠30° Ω and Y = 0.05 ∠-30° S
3. Z = 0.05 ∠30° Ω and Y = 20 ∠-30° S
4. Z = 0.05 ∠-30° Ω and Y = 20 ∠30° S

Answer 1

Correct Answer - Option 2 : Z = 20.0 ∠30° Ω and Y = 0.05 ∠-30° S

Concept:

Impedance:

• It is the measure of the opposition that a circuit presents to a current when a voltage is applied.
• It is the ratio of Voltage to Current.
• Impedance is a complex number, with the same units as resistance, for which the SI unit is the ohm (Ω).
• Its symbol is usually Z, and it may be represented by writing its magnitude and phase in the polar form |Z|∠θ.

Admittance:

• Admittance is a measure of how easily a circuit or device will allow a current to flow.
• It is defined as the reciprocal of impedance, analogous to how conductance & resistance are defined.
• The SI unit of admittance is the siemens (symbol S or  ℧(mho)).
• It is denoted as Y, and it may be represented by writing its magnitude and phase in the polar form |Y|∠θ.

Calculation:

Given

V = 100.0 ∠45° V  and I = 5.0 ∠15° A

Z = \({V\over I}\)

=\( {100∠45\over 5∠15}\) = 20∠ 30° Ω

Y = \({1\over Z} = {1\over 20\angle30}\) = 0.05 ∠-30° S