Question

A circuit consists of two impedances, Z₁ =20∠ 30ᵒ Ω and Z₂ = 25∠60ᵒ Ω, in parallel, supplied by a source voltage V=100∠60ᵒ volts. Determine the power triangle for each of the impedances and for the source.

Answer 1

To determine the power triangle for each impedance and the source in the given circuit, we need to calculate the power values for each impedance and then find the total power. The power triangle can then be drawn using these values.

Step-by-step explanation:

To determine the power triangle for each impedance and the source in the given circuit, we need to calculate the power values using the formulas:

Active Power (P) = I^2 * R

Reactive Power (Q) = I^2 * X

Apparent Power (S) = I^2 * Z

For impedance Z₁ = 20∠30ᵒ Ω, the active power P₁ = I₁^2 * R₁ and the reactive power Q₁ = I₁^2 * X₁ can be calculated. Similarly, for impedance Z₂ = 25∠60ᵒ Ω, the active power P₂ = I₂^2 * R₂ and the reactive power Q₂ = I₂^2 * X₂ can be calculated.

The total power in the parallel circuit is the sum of the individual powers. Therefore, the total power P_total = P₁ + P₂ and the total reactive power Q_total = Q₁ + Q₂. The total apparent power S_total can be calculated using the formula S_total = sqrt(P_total^2 + Q_total^2).

Finally, the power triangle for each impedance and the source can be drawn using the values of P, Q, and S as the base, perpendicular, and hypotenuse of the triangle, respectively.