An AC source with a maximum voltage of 150. V and f = 50.0 Hz is connected between points a and

step 1 Here we have R, RLC circuit, so L, and here we have a capacitance. This is resistance, inductor,

An AC source with a maximum voltage of 150. V and f = 50.0...

Key Concepts

Phasor Analysis

Phasor analysis is a technique used to simplify the study of AC circuits by representing sinusoidal functions as complex numbers (phasors). This allows for the straightforward handling of amplitude and phase relationships when summing voltages or currents, especially when there are multiple AC sources or when voltage drops across components must be calculated. Phasor representations transform the time-dependent differential equations into simpler algebraic forms in the frequency domain.

Root Mean Square (RMS) Voltage

RMS voltage is a key concept that represents the effective or equivalent DC voltage level in an AC circuit. For a sinusoidal waveform, the RMS value is obtained by dividing the peak voltage by the square root of two. This value is particularly useful because it correlates with the power delivered to resistive loads, making it a standard measure for comparing AC and DC circuits.

AC Sinusoidal Waveforms

AC sinusoidal waveforms describe how the voltage (or current) varies continuously and periodically over time. Such waveforms are characterized by their amplitude (maximum voltage), frequency (how often the waveform repeats per second), and phase. Understanding the sinusoidal variation is essential for analyzing and predicting the behavior of AC circuits since many calculations, including those for power and voltage distribution, rely on these waveform properties.

Voltage Division in AC Circuits

Voltage division refers to the way an applied voltage is distributed among various elements in a circuit. In AC circuits, this often involves not only the individual resistive values but also reactances when elements such as capacitors and inductors are involved. Understanding how voltage divides within a circuit is fundamental to accurately determining the potential differences between various circuit points.

Transcript

00:01 Here we have r, rlc circuit, so l, and here we have a capacitance.

00:10 This is resistance, inductor, and capacitance.

00:15 Resistance we have is 40 ooms, and the inductance we have is 185 millie henry, and the capacitance of 65 micro -faird.

00:28 This is point this is point a small a this is b this is c and this is d in part a we are asked to find what is the vrms through a b so resistance r we can find that v rms through resistance r by first finding the impedance z so impedance we have is the square root of r square plus xl minus xc square but we don't know xl and xc so we'll find xl and c and see also and substitute the value from there we'll find i rms so i rms will be simply vrms the total vrms divided by z impedance and from there then we can just find using irms and multiplying with the resistance 40 we can get v rms through this resistance so we are miss here so let's find xl so xl will be equal to 2 pi f times l substituting values 2 .3 .14 times frequency we have 50 times millie henry that is a 0 .4 this gives us inductance of reactants of a reactance of inductor that is a 58 .09 oms.

02:16 Similarly, xc will be equal to using the relation 1 over 2 pi fc.

02:24 Substuting value, xc we get here is 49 oms.

02:30 So we'll substitute those values, this one and this one in this equation.

02:36 Substituting those values we get the z to be square root of r r is a 40 oms so 40 square plus 58 .09 minus 49 whole square this gives us the impedance of 41 ooms so the ac source rms we have is ac source vrrms is vmax divided by square root of 2 this is 150 divided by square root of 2 this gives us ac source rms of 106 .1 volts from here then we can write i rms of a source is vrms divided by z this is 106 .1 divided by z we got is 41 this gives us i rms of source that is 2 .587 ampere...

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