Determine the peak voltage, the peak-to-peak voltage, the frequency (in hertz) and the angular f

step 1 Welcome to the problem number 31 .68. So in this question we are given an LCR circuit and all th

Determine the peak voltage, the peak-to-peak voltage, the...

Key Concepts

Angular Frequency

Angular frequency is the rate at which the waveform's phase changes, expressed in radians per second. It is related to the ordinary frequency by a factor of 2? and is an important concept in the analysis of oscillatory and wave phenomena.

Frequency

Frequency is the number of complete cycles or oscillations that occur per second, measured in hertz (Hz). It describes the periodicity of the waveform and is a critical parameter in determining how fast the signal repeats over time.

Peak Voltage

This is the maximum instantaneous value of a waveform measured from its zero or equilibrium position. It represents the highest amplitude reached by the signal and is fundamental in describing the signal's strength or amplitude characteristics.

Peak-to-Peak Voltage

This refers to the total voltage swing of the waveform, being the difference between its maximum and minimum values. It gives a complete measure of the signal's full range of variation over one cycle.

Transcript

00:01 Welcome to the problem number 31 .68.

00:05 So in this question we are given an lcr circuit and all the components are connected in series with an ac source so we need to find out at the angular frequency across the resistance so that the current is the maximum value and we also need to find out the angular frequency the voltage amplitude across the inductor is maximum and we also need to find out the angular frequency at which the voltage amplitude across the capacitance is maximum so we have three parts of this question.

00:37 So we have this circuit and we have to use this formula here.

00:42 We will use some other formulas but for the moment we have to use this formula so let's do the part a.

00:51 Before using this, so let's write some more information.

00:56 We know that the vl is equal to i xl and for having the maximum value.

01:05 So this would be vl over d omega equals to zero similarly we have vc equals to ixc so therefore we have dvc over d omega equals to zero i mean these are the quantities or these are the condition with all these figures so let's focus on the part a so we have i equals to v over z so we need vr equals to maximi we need we are equals to maximum we need we are equals to maximum for this maximum so we have that should be smallest so that we can have we are a maximum so that need to be smallest if you look at this formula r cannot be node r cannot be zero and this cannot be zero this cannot but xe minus xl can be zero so therefore this is our condition so this is the resident condition and which makes the vr maximum so the frequency comes out to be omega equals to omega l over one omega c because xc is equal to xl.

02:30 So this gives us omega equals to 1 over under root lc.

02:33 And this is also called omega node, which is the resident frequency...

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