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.

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Question

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SSC JE EE Previous Paper 12 (Held on: 24 March 2021 Evening)

Answer 1

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