Why do we need to use complex numbers when we analyze circuits that contain capacitors and inductors?

Complex numbers considerably make calculations easier. They turn inductors and capacitors to (sort of) resistors with complex resistances. So we get linear voltage-current relations instead of integrals and derivates. The main reason for using complex numbers is because they make calculations wayyyyy easier!

Why do we use complex numbers in circuit?

Complex numbers are convenient to represent and calculate both AC signals and impedance. The two dimensions, length and angle, allows us to calculate amplitude and phase together, and keep them consistent.

Are capacitors are essential for all circuits?

With increasing tech advances, capacitors have become essential components in almost every electronic device. They are capable of storing electrical charge, but not for a long period.

How complex numbers are useful in analyzing the AC circuits?

relation points directly to one reason why complex numbers make circuit analysis easier. Instead of representing a sinusoidal voltage or current as a sine or cosine function, we can represent it as an exponential. Exponentials are much easier to work with algebraically!

What are imaginary numbers used for in electricity?

Yes, electrical engineers use them as they are a mathematical representation of alternating current. They use ‘j’ to represent the square root of -1 (unlike mathematicians who use ‘i’) since in electrical engineering ‘i’ represents “current”.

Why do we need to use capacitors?

Capacitors are useful to reduce the voltage pulsation. When the high voltage is applied to the parallel circuit, the capacitor is charged, and on the other hand, it is discharged with the low voltage. While electricity flowing out is alternating current, most of electronic circuits work with direct current.

What are capacitors used for in real life?

The most common use for capacitors is energy storage. Additional uses include power conditioning, signal coupling or decoupling, electronic noise filtering, and remote sensing. Because of its varied applications, capacitors are used in a wide range of industries and have become a vital part of everyday life.

Why are complex numbers important in engineering?

Complex numbers are used in electrical engineering all the time, because Fourier transforms are used in understanding oscillations that occur both in alternating current and in signals modulated by electromagnetic waves.

Are the complex numbers a field of math?

The complex numbers are many other things beyond “a field” (they also have a geometric structure, and an analytic structure), but for their role as “numbers” we can initially stick to their algebraic behavior. So are there larger fields beyond the complex numbers?

Why do capacitors have a constant phase change but resistors don’t?

There are many reasons. But simplest answer is that ckt elements like capacitors and inductors introduce a phase change. But resistors do not. The phase change depends upon the element. What is constant is the fact that the elements are frequency dependant. These elements store energy.

Why is impedance of an RLC circuit complex?

Since $\\omega^2LC e1\\implies\\phi e0$, any definition of resistance we give for an RLC circuit has to use complex numbers to represent the LC parts’ phasing effects. This is why in general impedance is complex. Share Cite Improve this answer Follow answered Mar 21 ’20 at 7:57 J.G.J.G.

Why do we use imaginary numbers for current in reactive components?

Using imaginary numbers for current in reactive components just happens to make the maths a lot simpler. In AC circuits there is typically some phase difference between the voltage and the current.