Properties of Alternating Current: UNIZOR.COM - Physics4Teens - Electromagnetism
Channel: Zor Shekhtman on UNIZOR Education
Date: 2020-08-04

UNIZOR.COM - Physics through a Looking Glass of Mathematician

Properties of Alternating Current (AC)Let's talk about practical aspects of electricity. We use it to light up our homes, to move the motors that pump the water, to ignite the car engine etc.These are practical issues that must be resolved in the most efficient way.A short statement about alternating electric current is that it allows to do things easier and more efficient than direct electric current.In order to use electricity, we have to generate it. In most cases we convert mechanical movement into electricity at power plants. The most common way to transform mechanical motion into electricity is through induction. Recall, when we rotate a wire frame in the uniform magnetic field, the electric current is induced in the wire frame.The simplest mechanical motion that can be used on industrial scale is rotation. So, some mechanical source of energy can rotate the wire frame in a permanent magnetic field, which generates the electric current, that we can distribute through different circuits to different devices.As we know, induced electromotive force (EMF) in a wire frame, rotating in a magnetic field, depends on the rate of change of magnetic flux through this frame. In a simple case of a uniform magnetic field of intensity B and a wire frame rotating with constant angular speed ω around an axis perpendicular to the direction of magnetic field lines the magnetic flux going through a frame is changing with time, depending on the angle of rotation of a wire frame and the direction of the vector of magnetic field intensity.As was calculated in a lecture about a rotation of a wire frame, the magnetic flux going through a frame isΦ(t) = B·S·sin(ωt)where S=a·b is the area of a wire frame.The induced EMF U(t) in a wire frame equals to the rate of change of this flux:U(t) = −dΦ(t)/dt = −B·S·ω·cos(ωt)What's most important for us in this formula is that it shows the change of a magnitude and a direction of the induced EMF.The electric current resulting from this EMF that increases and decreases in absolute values and changes the direction in sinusoidal way is called alternating electric current.So, the most direct and effective way to produce an electric current causes this current to be alternating.The next step after generating the electricity is delivering it to consumers. This requires an extensive distribution network with very long wires and many branches.The amount of energy produced by a power plant per unit of time isPgen = U·IwhereU is the output voltageI is the output electric currentand all the above values are changing in time in case of alternating electric current.The amount of energy that is delivered to a user of electricity is less that this by the amount lost to overcome the resistance of wires that deliver the electricity, which is per unit of time equals toPlost = I²·RwhereI is the electric currentR is the resistance of wires.Using transformers, we can increase the voltage and, simultaneously, decrease the amperage of an electric current. We will do it right after the electricity is generated, which reduces the loss of energy in a wire that transmits electricity on a long distance.One of the important steps in the distribution of electricity is lowering the voltage, because we cannot connect any normal electric device, like a vacuum cleaner, to an outlet with hundreds of thousands of volts.This process of lowering the voltage is also easily accomplished using transformers.As we see, generation and distribution of alternating electric current is more efficient from practical standpoint than generation and distribution of direct electric current. That's why alternating electric current is so widely used.Most important property of the alternating electric current is its sinusoidal dependency on time.Voltage oscillates between −Umax and +Umax with certain frequency ω:U(t) = Umax·cos(ωt) orU(t) = Umax·sin(ωt)(both formulas, based on sin(ωt) and cos(ωt) describe the same behavior and differ only in when is the start time t=0).The maximum value Umax is called amplitude or peak voltage of an alternating current.The time during which the value of U(t) changes from its positive peak to another positive peak (or from negative peak to another negative peak) is called a period of an alternating electric current.If ω is the angular speed of rotation that caused the generation of alternating electric current, the period is, obviously, T=2π/ω.Frequency is the number of periods per unit of time: f=1/T=ω/2π and the unit of frequency is hertz (Hz), so the frequency of 50Hz means that the voltage changes from one positive peak to another 50 times per second..The amperage behaves, according to the Ohm's Law, similarly, oscillating between −Imax and +Imax with the same as voltage frequency ω:I(t) = Imax·cos(ωt) orI(t) = Imax·sin(ωt)(depending on when is the start time t=0)where Imax = Umax / R and R is the resistance of the circuit.