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