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  • If we apply an AC voltage, the frequency of the voltage affects the amount of current that will flow.

  • Inductors, capacitors, and resistors all react differently to AC voltage.

  • But, in all three cases, the frequency of the AC current will be exactly equal to the frequency of the voltage.

  • Let us call the voltage at this point the "Input Voltage".

  • This is the voltage that we control.

  • In the case of an ideal resistor,

  • the current that flows is always proportional to the difference in the voltage values at the two sides of the resistor.

  • This means that if the only components in our circuits are ideal resistors,

  • then the amplitude of the current that flows is independent of the voltage's frequency.

  • Now, suppose we replace the resistor on the right with a capacitor.

  • Once the capacitor is charged, both sides of the resistor will have the same voltage, and no current will flow.

  • Current flows only if we change the value of the input voltage.

  • The amount of current that flows depends on the difference in the voltage values of the two sides of the resistor.

  • If we change the value of the input voltage slowly,

  • then the voltage values of the two sides of the resistor will tend to stay at about the same voltage.

  • This means that only a small amount of current will flow through this circuit at low frequency.

  • At high frequency, a larger amount of current will flow.

  • This is because if we vary the input voltage quickly as shown,

  • the capacitor never has enough time to charge, and the voltage across it always stays close to zero.

  • Having a voltage across the capacitor that is always close to zero

  • allows a larger voltage difference between the two ends of the resistor, allowing more current to flow.

  • Since the voltage across the capacitor does not have the ability to change instantaneously,

  • the voltage across the capacitor changes after the current changes.

  • Let's turn off the input voltage.

  • Now let's replace the capacitor with an inductor.

  • An inductor exerts a force preventing the current flowing through it from changing instantaneously.

  • If the input voltage is constant, then the inductor will not exert any forces, and it will therefore not impede the flow of current.

  • If the input voltage changes, the inductor will initially try to keep the current through it at the same value as before.

  • After we change the voltage, we need to wait for the current to change.

  • After the current changes, the inductor then wants to keep the current at this new value.

  • If we change the input voltage very rapidly as shown, the current will not have enough time to change.

  • This means that only a small amount of current will flow through the inductor at high frequency.

  • At low frequency, more current will flow.

  • In this sense, an inductor has the opposite behavior of a capacitor.

  • Also, whereas the voltage across a capacitor can't change instantaneously,

  • for an inductor it is the current that can't change instantaneously.

  • This means that for an inductor, the current changes after the voltage changes.

  • The frequency of the input voltage is only one of the factors that determines how much the inductor will impede the flow of current.

  • Another factor is the amount of inductance the inductor has.

  • If the inductor has a higher inductance, then a smaller amount of AC current will flow through it.

  • This is because with a higher inductance,

  • the inductor will exert a greater force trying to keep the current flowing through it constant.

  • In this example, even though we have a low frequency,

  • we still have a small amount of AC current flowing due to the fact that the value of the inductance is high.

  • Increasing the capacitance of a capacitor has the opposite effect of increasing the inductance of an inductor.

  • If a capacitor has a higher capacitance, then a larger amount of AC current will flow through it.

  • This is due to the fact that with a higher capacitance, the capacitor charges and discharges more slowly.

  • Therefore, in this case, the voltage across the capacitor stays close to zero,

  • thereby allowing a larger difference in voltage to develop at the two ends of the resistor,

  • thereby allowing more current to flow.

If we apply an AC voltage, the frequency of the voltage affects the amount of current that will flow.

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