Clutch Prep is now a part of Pearson
Ch 32: Alternating CurrentWorksheetSee all chapters
All Chapters
Ch 01: Intro to Physics; Units
Ch 02: 1D Motion / Kinematics
Ch 03: Vectors
Ch 04: 2D Kinematics
Ch 05: Projectile Motion
Ch 06: Intro to Forces (Dynamics)
Ch 07: Friction, Inclines, Systems
Ch 08: Centripetal Forces & Gravitation
Ch 09: Work & Energy
Ch 10: Conservation of Energy
Ch 11: Momentum & Impulse
Ch 12: Rotational Kinematics
Ch 13: Rotational Inertia & Energy
Ch 14: Torque & Rotational Dynamics
Ch 15: Rotational Equilibrium
Ch 16: Angular Momentum
Ch 17: Periodic Motion
Ch 19: Waves & Sound
Ch 20: Fluid Mechanics
Ch 21: Heat and Temperature
Ch 22: Kinetic Theory of Ideal Gases
Ch 23: The First Law of Thermodynamics
Ch 24: The Second Law of Thermodynamics
Ch 25: Electric Force & Field; Gauss' Law
Ch 26: Electric Potential
Ch 27: Capacitors & Dielectrics
Ch 28: Resistors & DC Circuits
Ch 29: Magnetic Fields and Forces
Ch 30: Sources of Magnetic Field
Ch 31: Induction and Inductance
Ch 32: Alternating Current
Ch 33: Electromagnetic Waves
Ch 34: Geometric Optics
Ch 35: Wave Optics
Ch 37: Special Relativity
Ch 38: Particle-Wave Duality
Ch 39: Atomic Structure
Ch 40: Nuclear Physics
Ch 41: Quantum Mechanics
Sections
Phasors
Impedance in AC Circuits
Alternating Voltages and Currents
Inductors in AC Circuits
Capacitors in AC Circuits
Power in AC Circuits
Resistors in AC Circuits
Series LRC Circuits
RMS Current and Voltage
Phasors for Inductors
Phasors for Capacitors
Phasors for Resistors
Resonance in Series LRC Circuits
Learn
Next SectionPhasors for Resistors

Concept #1: Phasors for Capacitors

Transcript

Hey guys, in this video we're going to talk about phasors for capacitors in AC circuits. So the current phasor and the voltage phasor for a capacitor in the AC circuit. Alright, let's get to it. Remember guys that there are two functions that describe the voltage and a current across a capacitor at any time T in an AC circuit. These are given by this. Because the angle for each of them is different, we have theta equals omega T here and we are some other angle which I'll call theta prime equals omega T minus Pi over 2. Because the cosines each have a different angle we are saying that they are out of phase and in fact the voltage lags the current. This is very different than the phasors we saw for resistors which were in phase because both functions had the same angle omega T. If we look at the three phasor diagrams that I drew, the first one we have the current at an angle omega T, right? That is the angle of the current. In the second one we have omega T minus Pi over 2 as the angle for the voltage that takes us all the way down to the negatives because omega T itself as we can see is less than Pi for 2 so that takes us into the negatives and that also means that these have to have a 90 degree angle. This is just omega T which is the angle for the current minus 90 degrees so they're separated by 90 degrees. So whenever you draw the phasor diagram which includes both the current and the voltage phasors for a capacitor, you have to draw it with the voltage lagging the current or the current leading the voltage. It's very important that you guys memorise that the current leads the voltage or the voltage lags the current for a capacitor and that is the thing to take away from this that the voltage across a capacitor always lags the current in the capacitor circuit.

Let's do a quick example. An AC source is connected to a capacitor. At a particular instant in time, the voltage across the capacitor is positive and increasing in magnitude. Draw the phasors for the voltage and the current that correspond to this time. Now whenever a phasor is increasing in magnitude it's because as it rotates it gets closer to a horizontal axis. As it gets closer and closer to that horizontal axis its projection onto that axis gets larger and larger and larger and remember the projection onto the horizontal axis tells us the value of that phasor. Now if this phasor is going to be positive it needs to be pointing to the right and if it's going to be increasing in magnitude it need to be pointing to the right and moving towards the X axis. Since phasors always rotate counterclockwise that means that the voltage phasor has to be here and it's rotating like this. So it's positive because it points to the right and it's increasing in magnitude because as it gets closer to that horizontal axis more and more and more of it points horizontally until it's on the horizontal axis, now it's at a maximum, and then as it moves away from the horizontal axis it decreases and decreases in value until it's straight up and it's zero. Now if the voltage is here, the current is 90 degrees ahead of it so the current is going to be here, this is a current through a capacitor, this is the voltage of the capacitor and this is a 90 degree angle. So this is what the phasor diagram looks like if the voltage is positive and increasing. Alright guys, that wraps up our discussion on phasors with capacitors. Thanks for watching.

Practice: An AC source operates at a maximum voltage of 60 V and is connected to a 0.7 mF capacitor. If the current across the capacitor is i(t) = iMAX cos[(100 s−1 )t], 

a) What is iMAX? 

b) Draw the phasors for voltage across the capacitor and current in the circuit at t = 0.02 s. Assume that the current phasor begins at 0°.

Previous SectionPhasors for Inductors
Next SectionPhasors for Resistors