I need help in breaking down the textbook explanation of calculating self-induced voltage across an inducance. The formula is induced voltage equals inductance (henrys) times change of current (amperes) divided by time (per second). My questions begin with finding the variables, such as henrys. Where can the henrys be found or calculated? Secondly, where can amperes per second be found or calculated? I have ever used amperes per second, please explain. Also if you have some examples, please post.
Understanding Voltage and Current in an inductive AC circuit
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It is not something that is generally calculated, except perhaps as a test question. But in a test, they would give you the numbers that you need, and expect you to be able to apply the formula.
In real life, the number of Henrys that an inductor would have is a function of the type and size of wire, the number of turns of wire, the material around which the wire is wound, and a few other things. To get the number of Henrys, you read the label on the device.
To understand ?amperes per second,? you have to realize you are dealing with an instant-by-instant process. In other words, you look at the current at various points within each cycle, from zero amps to max amps to zero amps to max negative amps and back to zero, 60 times each second. Look at the amount of change in amps from just to the left of the peak to just to the right of the peak. Over that short amount of time, the amps do not change much (i.e., the curve is mostly flat). Now look at the amount of change in amps from just to the left of the point of amps = 0 to just to the right of that point. Over that short amount of time, the amps change much more than they do at the peak (i.e., the curve is a steep line going upwards). Thus, instant-by-instant not only are the amount of amps changing, but the ?change in amps per unit time? is also changing. It turns out that since the amps themselves follow the shape of a sine wave, the ?change in amps per unit time? also follows a sine wave. The actual math to calculate this process lies within the realm of calculus, and I?ll not present it here.
In real life, the number of Henrys that an inductor would have is a function of the type and size of wire, the number of turns of wire, the material around which the wire is wound, and a few other things. To get the number of Henrys, you read the label on the device.
To understand ?amperes per second,? you have to realize you are dealing with an instant-by-instant process. In other words, you look at the current at various points within each cycle, from zero amps to max amps to zero amps to max negative amps and back to zero, 60 times each second. Look at the amount of change in amps from just to the left of the peak to just to the right of the peak. Over that short amount of time, the amps do not change much (i.e., the curve is mostly flat). Now look at the amount of change in amps from just to the left of the point of amps = 0 to just to the right of that point. Over that short amount of time, the amps change much more than they do at the peak (i.e., the curve is a steep line going upwards). Thus, instant-by-instant not only are the amount of amps changing, but the ?change in amps per unit time? is also changing. It turns out that since the amps themselves follow the shape of a sine wave, the ?change in amps per unit time? also follows a sine wave. The actual math to calculate this process lies within the realm of calculus, and I?ll not present it here.
Inductive Reactance:
Inductive Reactance:
From the fundamental formula we can develop formulas for reactance and impedance for use with RMS voltages and currents--steady state solutions.
For sinusoidal currents, di/dt is constantly changing, and the voltage across the inductor is also changing, and it turns out that the this voltage is also sinusoidal. The RMS voltage and current are related by the formula:
Vrms/Irms = Xl = 2*pi*f*L
Where Xl is the reactance in Ohms, f is the frequency in Herz, and L is the inductance in Henrys.
Please note that the current lags the voltage by 90 degrees in an ideal inductor, but reactance is a a magnitude which carries no phase angle. Impedance on the other hand is a complex number which contains both a magnitude and phase angle.
Capacitive reactance may also be calculated, but we will save that for another thread.
Inductive Reactance:
From the fundamental formula we can develop formulas for reactance and impedance for use with RMS voltages and currents--steady state solutions.
For sinusoidal currents, di/dt is constantly changing, and the voltage across the inductor is also changing, and it turns out that the this voltage is also sinusoidal. The RMS voltage and current are related by the formula:
Vrms/Irms = Xl = 2*pi*f*L
Where Xl is the reactance in Ohms, f is the frequency in Herz, and L is the inductance in Henrys.
Please note that the current lags the voltage by 90 degrees in an ideal inductor, but reactance is a a magnitude which carries no phase angle. Impedance on the other hand is a complex number which contains both a magnitude and phase angle.
Capacitive reactance may also be calculated, but we will save that for another thread.
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