Question
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i) You are testing the voltage across a capacitor in an AC circuit. The instrument
you are using indicates this voltage to have a magnitude of 100 V and a phase
angle of 45 degrees. Convert this voltage into a complex number.

Ask by Davies Olson. in the United Kingdom
Mar 14,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The voltage can be expressed as .

Solution

  1. The given voltage magnitude is V and the phase angle is .
  2. In polar form, the voltage is written as:
  3. To convert to rectangular form, we use the formulas:
    where V and .
  4. Evaluate the trigonometric functions:
  5. Substitute the values:
  6. Simplify the expression:
Thus, the complex representation of the voltage is:

Answered by UpStudy AI and reviewed by a Professional Tutor

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Simplify this solution

The Deep Dive

To convert the given voltage into a complex number, we start with the polar form: . We can convert this to rectangular form using the formula , where is the magnitude and is the phase angle.
Calculating the real and imaginary parts:
Real part:
Imaginary part:
So, the voltage in complex form is V.
Now you have a vibrant complex number representing your voltage, perfect for analyzing in the world of AC circuits!

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