Question

question 14 which of the following is not a correct formula for solving unknown values in an inductive circuit? ○ cos θ = reactive power/apparent power ○ true power/apparent power = r/z ○ cos θ = r/z ○ cos θ = true power/apparent power

Explanation:

To determine the incorrect formula for an inductive circuit, we analyze each option:

1. Recall the power triangle and impedance triangle relationships:

• True power (\(P\)) = \(I^2R\), Apparent power (\(S\)) = \(I^2Z\), Reactive power (\(Q\)) = \(I^2X_L\) (for inductive circuits).
• The power factor \(\cos\theta\) is defined as \(\frac{\text{true power}}{\text{apparent power}}\) (since \(P = S\cos\theta\)), so \(\cos\theta=\frac{P}{S}\).
• From the impedance triangle, \(\cos\theta=\frac{R}{Z}\) (since \(R = Z\cos\theta\)).
• Reactive power \(Q = S\sin\theta\), so \(\sin\theta=\frac{Q}{S}\), not \(\cos\theta\).

1. Analyze each option:

• Option 1: \(\cos\theta=\frac{\text{reactive power}}{\text{apparent power}}\) → Reactive power is \(Q = S\sin\theta\), so \(\frac{Q}{S}=\sin\theta\), not \(\cos\theta\). This is incorrect.
• Option 2: \(\frac{\text{true power}}{\text{apparent power}}=\frac{R}{Z}\) → \(\frac{P}{S}=\frac{I^2R}{I^2Z}=\frac{R}{Z}\), which matches \(\cos\theta=\frac{R}{Z}\). Correct.
• Option 3: \(\cos\theta=\frac{R}{Z}\) → From impedance triangle (adjacent/hypotenuse), correct.
• Option 4: \(\cos\theta=\frac{\text{true power}}{\text{apparent power}}\) → By definition of power factor, correct.

Answer:

A. \(\boldsymbol{\cos \theta = \text{reactive power/apparent power}}\)