By now, you must be familiar with direct current (DC), which is an electric current that flows in only one direction. But the type of electricity that really powers our homes, industries and most electrical appliances is the alternating current (AC). Understanding this concept will help you answer your Physics examinations accurately. To get the best understanding, request for practice questions on the application of both DC and AC concepts from your school or Physics tuition. To start you off, here is an explanation of the concept of AC currents:
In contrast to DC current, AC current keeps reversing its direction. The polarity of the electromotive force (e.m.f.) changes with time for the AC electricity. This means that the direction of the flow of current in an AC electrical circuit varies in a periodic manner, and the direction of that charge carriers’ flow changes back and forth.
AC Current Waveform
The waveform of AC current flowing in an electrical circuit is usually represented graphically as a sine wave. The sinusoidal AC current waveform is represented by the equation:
I = Io.sin?t
Where,
I is the AC current in the resistor.
Io is the maximum current flow during the cycle (also known as the amplitude of the AC signal).
?t is the angular frequency of the sinusoidal wave form and is equal to 2pf rad/sec, where f is the frequency which is equal to 1/T, where T is the time taken to complete one variation cycle.
Root Mean Square Value
The root mean square (r.m.s) value is an important concept in AC electricity. When you use an AC ammeter to measure the amount of current flowing in a circuit, it is this value you will see. It is also known as the effective current of an AC circuit
The r.m.s. is the amount of steady direct current that is required to convert electrical energy into other forms of energy at the same average rate as the AC current in a given resistance.
Consider an AC circuit and a DC circuit with the resistance (R).
The power dissipated by a DC circuit with a resistance R:
Pdc = I2dc R
The average (mean) power dissipated by an AC circuit with a resistance R:
<Pac > = <I2ac > R
Suppose that the two circuits have the same resistance and are dissipating power at the same rate.
I2dc R = <I2ac > R
Or I2dc = <I2ac >
Or Idc = square root of <I2ac > = Irms
Thus, steady Idc is equivalent to the square root of the mean of the square of Iac.
You can calculate r.m.s. value of an AC current in simple steps:
- Take the current reading and square it
- Take the mean (average) value of the current
- Square root the mean value
Irms = Io / Where Io is the peak current.
Power dissipation in a resistive load
In an AC circuit, the current and the voltage are in phase and both of them vary sinusoidally with the same angular velocity.
Let’s say that the sinusoidal voltage applied across a resistance of R is V = Vo. sin?t, where ?t is the angular frequency. We know that the current in the resistor R is I = Io.sin?t.
The power dissipated by the resistor is:
P = IV
Or P = (Io.sin?t) (Vo. sin?t)
Or P = Io.Vo. sin2?t
Or P = Po.sin2?t Where Po is the maximum power or peak power.
Now you can calculate the mean power using the following equation:
<P> = < Io.Vo. sin2?t>
Or <P> = Io.Vo <sin2?t>
Or <P> =
Or <P> = Po
Mean power is also equal to
<P> = I2rms R
If you have found this concept too confusing or a tough nut to crack, you should consider taking up a Physics tuition to boost your understanding. Make sure to choose one that has qualified and experienced tutors who can suit your learning style.
