Question

The equation Θ = tan⁻¹ (wC/G) gives the phase angle of impedance in the parallel portion of a distributed constant circuit. Find Θ if w = 260 radians per second, C = 0.02 uF per kilometer, and G = 1.27 μsiemens per kilometer.

A. 53.02°
B. 33.05°
C. 62.57°
D. 71.29°

Answer 1

To find the phase angle of impedance given the frequency, capacitance, and conductance, we use the provided equation and convert units to their base form. Despite performing these calculations, the result obtained does not match the provided options.

Step-by-step explanation:

To find the phase angle ϴ of the impedance in a parallel portion of a distributed constant circuit, we can use the equation ϴ = tan⁻¹ (wC/G). Plugging in the given values:

• ω (omega) = 260 radians per second
• C (capacitance) = 0.02 µF/km = 0.02 × 10⁻¶ F/km
• G (conductance) = 1.27 µsiemens/km = 1.27 × 10⁻¶ siemens/km

First, we need to convert the units of C and G to their base units:

• C = 0.02 x 10⁻¶ F/km = 2 x 10⁻¸ F/km
• G = 1.27 x 10⁻¶ siemens/km = 1.27 x 10⁻¶ S/km

Now calculate the tangent inverse:

• ϴ = tan⁻¹ (260 x 2 x 10⁻¸/1.27 x 10⁻¶)
• ϴ = tan⁻¹ (0.4094488)
• ϴ ≈ 22.43°

However, this result isn't close to any of the options provided, indicating either a possible miscalculation or a missing crucial piece of information to correctly answer the question.