Question

A circuit consists of two impedances Z₁= 20∠30^oΩand Z₂= 25∠60^oV , in parallel, supply by a source voltage V =100∠60^oV . Determine the power triangle for each of the impedances and for the source.

Short answer

Therfeore, the power triangle for impedance20∠30^oΩ is drawn below:

The power triangle for impedance 20∠30^oΩ is drawn below:

The power triangle for voltage source is:

Step-by-step solution

Determine the formulas

Write the formula of current

I =$\frac{\mathrm{V}}{\mathrm{Z}}$.....................(1)

Write the formula of apparent power

Write the formula of power factor

p.f =cosθ ...............(3)

Determine the power factor.

Consider that the I∠$\varnothing$₁and I₂∠$\varnothing$₂are the branch currents through impedances 20∠ 30^oΩ and 25∠ 60^oΩ These currents are calculated as,

Solve for the branch current I₁∠ $\varnothing$₁

Solve for the branch current I₁∠$\varnothing$₂

The angle between the source voltage and branch current

Hence, the power factor is,

pf₂=cos60^o

=0.5

Determine the active power, reactive power and apparent power

The apparent power for impedance 1 using equation (2) is calculated as,

Substitute the values and solve.

The apparent power for impedance 2 is calculated as,

Substitute the values and solve.

Therfeore, the power triangle for impedance 20∠30^o is drawn below:

The power triangle for impedance 25∠60^o Ω is drawn below:

Draw power triangle for source

The total active power supplied by source is,

The total reactive power supplied by source is,

The total apparent power supplied by source is,

The total current supplied by the source is,

The angle between source voltage and source current is,

The power triangle of voltage source is,