Help w/ Circuit Theory: Complex Numbers & Voltage

In summary, the individual is working on a circuit theory assignment and is seeking confirmation on their approach. They have a voltage value of 120 /_0 and are wondering if they can assume that Arctan(a/b) = 0, resulting in V = 120 in phase. They also have a v value of √2 x 415cos(100πt) and are questioning if they can say "t = 0" and end up with v = √2 x 415cos(0) where Cos(0) = 1. They are unsure if this is correct and if they are missing any steps.
  • #1
Toolkit
2
2
Thread moved from the technical forums, so no Homework Template is shown
Hi,

I'm working on an assignment for circuit theory, and I'm wondering if someone could let me know if I'm heading in the right direction?

1) I have a voltage value of 120 /_0 (polar form), from this can I assume that Arctan (a/b) =0, so voltage =120 in phase?

Therefore, V =120+J0, where V = a+jb

2) If I have a v = √2 x415cos(100πt) , basically can I say that "t = 0" , I end up with v = √2x415cos (0),

where Cos(0) = 1

is this correct, or am I missing something?

Thanks,

Colin
 
Physics news on Phys.org
  • #2
correct
 
  • #3
You are heading in the right direction.
Check when you should be using Atan( a/b ), Atan( b/a ) or the Atan2( b, a ).
 

FAQ: Help w/ Circuit Theory: Complex Numbers & Voltage

1. What are complex numbers and how are they used in circuit theory?

Complex numbers are numbers that have both a real part and an imaginary part. In circuit theory, they are used to represent the amplitude and phase of a voltage or current signal. They are particularly useful in AC circuits, where the voltage and current are constantly changing direction.

2. How do complex numbers help in understanding voltage in circuits?

Complex numbers are used to represent the voltage in a circuit as a phasor, which is a rotating vector in the complex plane. This allows us to visualize the amplitude and phase of the voltage signal, which is important in analyzing the behavior of AC circuits.

3. What is the relationship between complex numbers and impedance?

Impedance is a measure of the opposition to the flow of an AC current in a circuit. It is represented by a complex number, where the real part represents the resistance and the imaginary part represents the reactance. This allows us to calculate the total impedance of a circuit using complex number arithmetic.

4. How do you calculate the voltage across a component using complex numbers?

To calculate the voltage across a component in an AC circuit, you can use Ohm's law (V=IR) with the complex impedance of the component. This will give you a complex number representing the amplitude and phase of the voltage signal. You can then convert this back to a time-domain voltage using the inverse Fourier transform.

5. Can you give an example of using complex numbers in voltage analysis of a circuit?

Sure! Let's say we have a series circuit with a resistor and an inductor. The voltage across the resistor is given by V=IR, where R is the resistance and I is the current. The voltage across the inductor is given by V=jωL, where j is the imaginary unit, ω is the angular frequency, and L is the inductance. To find the total voltage in the circuit, we can add these two complex numbers together (V=IR+jωL). This allows us to calculate the amplitude and phase of the total voltage, which can help us understand the behavior of the circuit.

Similar threads

Calculation of current in driven series RLC circuit
Replies
8
Views
735
Write boolean expression describing this circuit
Replies
4
Views
647
Understanding example in Wikipedia entry for open circuit voltage
Replies
3
Views
996
Solving Current & Power in 4 & 3 Wire Circuits
Replies
9
Views
2K
Question about complex power in three phase circuits
Replies
2
Views
2K
How to Determine Values of L and C in a Series RLC Circuit at Resonance?
Replies
8
Views
1K
Why can we add impedances in series?
Replies
4
Views
639
What does a Zener diode do in a circuit with non-ideal voltage source?
Replies
3
Views
505
Ohm's Law - Finding Source Voltage
Replies
3
Views
935
Two networks described by v-i graph: Find voltages when interconnected
Replies
1
Views
739

Hot Threads

Recent Insights

Back
Top