Two elements are connected in series as shown in Fig. 9.40 . If i=12 cos(2 t-30^∘) A, find the e

step 1 Hello, so let's solve this problem. So in this problem we have to find out the values of the cir

Two elements are connected in series as shown in Fig. 9.40 ....

Key Concepts

Conversion Between Time Domain and Phasors

Converting between the time domain and phasors involves using Euler's formula to represent sinusoidal functions as complex exponentials. This conversion is crucial for simplifying the analysis of linear circuits under steady-state sinusoidal excitation by enabling the application of algebraic methods instead of solving differential equations.

Series AC Circuit Analysis

Series AC circuit analysis involves studying circuits where components are connected end-to-end with the same current flowing through each element. In these circuits, the total impedance is found by summing the individual complex impedances, which allows for straightforward calculation of the overall circuit behavior.

Impedance

Impedance extends the concept of resistance to AC circuits by incorporating both resistive and reactive effects. It is a complex quantity that represents how a circuit element opposes current flow, with the real part denoting resistance and the imaginary part representing reactance.

Phasor Representation

Phasor representation is the method of converting time?varying sinusoidal signals into complex numbers that capture both magnitude and phase. This method simplifies the analysis of AC circuits by turning differential equations into algebraic equations, making it easier to manipulate and combine signals.

Transcript

00:01 Hello, so let's solve this problem.

00:04 So in this problem we have to find out the values of the circuit element separately and the given values are the voltage and the current.

00:15 So what we have to find out is the circuit element separate.

00:18 First of all, we have to identify what are these circuit elements.

00:22 So i am just writing two important points which we should keep in our mind.

00:27 First thing is if the current is leading from the voltage is the leading from the voltage then the impedance will be the current is leading the impedance will be capacitive and if the current is lagging from the voltage then the impedance will be inductive right so now first of all inductive right inductive right so first of all how to identify whether the current is lagging or leading so look at these equations very carefully right so if you will look at over here what you have to find out is we have to first identify or we have to compare it with the standard equation so if we compare what we have found is this is our omega -t and this is our this is omega -t what? right, give me one second.

01:36 This is our, i'm writing over here, right? this is our omega t and this is our five.

01:44 Similarly over here, this is our omega t and this is our five, right? so if you look at over here is the current is, if you are looking over here, there's a phase difference by the face, the voltage is leading from the current.

02:04 Is lagging from the border.

02:06 So if you look at these points, if the current is lagging, if the current is lagging, then our impedance will be inductive.

02:15 It means one of the element is inductor and one of the element is resistance.

02:25 So if this is our, let's suppose this is our resistance and this is our inductor.

02:32 So this is our x -m.

02:35 Now we have to find out this.

02:36 Values of these r and excel separately.

02:40 So if you look at this, this is our maximum voltage and this is our maximum current.

02:48 The most easiest way to get the magnitude of the inductance is use this formula which i am writing over here.

02:56 The magnitude of z can be written as and we are only interested for the magnitude because we have to find out the value, not the whole vector.

03:04 So the magnitude of z is it can be written as...

Please give Ace some feedback