A 400-Ωresistor and a 6.00-capacitor are connected in parallel to an ac generator that supplies

step 1 Welcome to the problem number 31 .56. So this is chapter 31 alternating current. In this questio

A 400-Ωresistor and a 6.00-capacitor are connected in...

A 400-$\Omega$ resistor and a 6.00-$\mu$F capacitor are connected in parallel to an ac generator that supplies an rms voltage of 180 V at an angular frequency of 360 rad/s. Use the results of Problem 31.54. Note that since there is no inductor in this circuit, the 1/$\omega$L term is not present in the expression for 1/Z. Find (a) the current amplitude in the resistor; (b) the current amplitude in the capacitor; (c) the phase angle of the source current with respect to the source voltage; (d) the amplitude of the current through the generator. (e) Does the source current lag or lead the source voltage?

A 400-$\Omega$ resistor and a 6.00-$\mu$F capacitor are connected in parallel to an ac generator that supplies an rms voltage of 180 V at an angular frequency of 360 rad/s. Use the results of
Problem 31.54. Note that since there is no inductor in this circuit, the 1/$\omega$L term is not present in the expression for 1/Z. Find (a) the current amplitude in the resistor; (b) the current amplitude in the
capacitor; (c) the phase angle of the source current with respect to the source voltage; (d) the amplitude of the current through the generator. (e) Does the source current lag or lead the source
voltage?

Key Concepts

AC Circuit Analysis

This concept involves examining circuits powered by alternating current, where voltages and currents vary sinusoidally with time. It includes using RMS (root mean square) values, understanding frequency, and recognizing how circuit components respond to AC signals.

Resistor Behavior in AC Circuits

In AC circuits, resistors obey Ohm’s law just as in DC circuits, where the voltage across the resistor is in phase with the current. The current amplitude can be directly calculated from the applied voltage and the resistance using the ratio I = V/R.

Capacitive Reactance

Capacitive reactance is the measure of a capacitor’s opposition to changes in voltage in an AC circuit. It is calculated as X_C = 1/(?C), where ? is the angular frequency. Unlike resistors, the current through a capacitor leads the voltage by 90 degrees.

Impedance in AC Circuits

Impedance is the total opposition that a circuit offers to AC, combining both resistance and reactance into a complex quantity. It characterizes both the magnitude and the phase difference between the applied voltage and the resulting current.

Phasor Representation and Phase Angle

Phasor analysis simplifies the handling of sinusoidally varying quantities by representing them as complex vectors in the frequency domain. This allows for straightforward addition of currents and voltages, determination of phase differences, and understanding whether the overall current leads or lags the voltage.

Transcript

00:01 Welcome to the problem number 31 .56.

00:03 So this is chapter 31 alternating current.

00:06 In this question we are given a rc circuit and r and c are connected in parallel and they're connected with ac generator.

00:16 So this is an ac source and this supplies 180 volt which is an rms voltage and the frequency of this ac source is 360 radian per second.

00:27 We have to use the result of the 31 .5 for problem and and we are given that the resistance is our 400 -hom and capacitance is 6 microferradi so this part consists of five parts a b c d e we will solve one part one by one so let's tackle the first part a so we have to use the problem number 31 .54 so we have fee equals to root hundred two vrms so voltage amplitude is equal to root 2 times 180.

01:14 So this gives us 254 .6 volt.

01:23 Now finding out the current through the resistance, so which is equals to v over r.

01:30 So we have 254 .6 over 400 o 'ong.

01:37 So this gives us current passing through the resistance.

01:40 So this is the amplitude of the current.

01:47 So that's our a part.

01:49 Now we go to the p part.

01:55 We have ic equals to v over omega c.

02:03 As we know that xc is equals to 1 over omega c.

02:12 Sorry, yeah.

02:15 Pardon me? so this should be omega c right...