**These notes are for tonight’s Elmer Net:**

**Extra Class License Manual (ECLM)**

**4.3-2**

**DC vs. AC**

We analyze the behavior of components using the application of instantaneous DC. This helps us better understand how the component responds to a change in voltage. Understanding how the component responds to the change helps us understand how it responds to AC. The use of inductors (L) and capacitors (C) always involves responding to changes in voltage.

A capacitor essentially becomes an open circuit to DC after 5 time constants, TC = RC. An inductor becomes a short circuit to DC after 5 time constants, TC=RL. However, when there are changes they both become variable components. They respond when the applied voltage changes and when the frequency changes. Additionally, the compents themselves may be variable components. The folrmulas, below, show that if the value of the component or the frequency of the applied voltage changes, the reactance of that component changes. Changing the frequency can have the same effect as increasing or decreasing the value of the actual component.

Review the following formulas again as they will be used going forward. 2pi is just a representation of points in time of a cycle. There are 2pi radians in a circle, about 57.3 degrees per radian. F is the frequency and should not equal 0. C is the capacitance in farads and L is the inductance in Henries. Reactance is the resistance or opposition to AC.

**Phase angle**

As previously discussed, a signal, like a sine wave, follows a cycle, it repeats itself. The time it takes to complete one cycle is the period. The number of times the cycle completes in one second is its frequency 1/period=frequency; 1/frequency = period.

If Voltage and Current change simultaneously in the same direction during the cycle, they are "in phase". Notice the amplitudes may not be the same but the 0 crossing points and peaks are identical. This is the typical response for a non-inductive resistor. There is typically no phase difference between the Voltage and Current in a purely resistive compnent.

**Phase angle in Inductors**

We learned that and inductor opposes a change in current, usually a result of a change in voltage at some point in the circuit. Initially the current is very low and the voltage measured across the inductor is high. This is because the change is a high frequency, it is changing very fast from 0 to applied voltage. The formula above shows that if the frequency is high, the XL will also be high and the current will be low. This means there is a phase difference. If the voltage is at a high and the current is at a 0, we have a 90 degree difference, assumig a sine wave.

In the graphic below, point a shows at time 0, the voltage is high but the current if low. at point a, the voltage has decreased to 0v while the current has increased to a peak. The difference in time between 0 and point a is 1/4 of a cycle or 90 degrees. (360/4=90).

In this case, we say the Voltage is Leading the current by 90 degrees. The voltage reaches its peak 90 degrees in time before the current. You can also see the difference between points c and d. a

at c, the voltage has already reached 0 on the time line but the current is still at the negative peak. At point d, the current has come up to 0 but the voltage is already at the positive peak.

We can note this as ELI, Electromotive Force (E) leads the current (I).

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**Phase angle in capacitors**

**As we have learned Capacitors are the OPPOSITE of inductors. Referring to the graphic below, at point 0 the voltage is at maximum while the current has already passed the maximum current and is at 0. At point c, we see that voltage is 0 but the current is already at the positive peak. The current through the divice is ahead of the voltage.**

**How does this happen? We learned that when a DC voltage is applied to a capacitor, the current immediately hace a high current as the XC is low. In the formula, the f (frequency) is in the denominator making it a small fraction. Cuttent is very high but the voltage measured across the capacitor is low. After 5 time constants, the capacitor is fully charged and the current drops to 0 while the voltage is maximum. We say that I current is leading E (Electromotive Force - V). The notation is ICE.**

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**Memory Aid: ELI the ICE man.**

E5B09 (D)

What is the relationship between the AC current through a capacitor and the voltage across a capacitor?

A. Voltage and current are in phase

B. Voltage and current are 180 degrees out of phase

C. Voltage leads current by 90 degrees

D. Current leads voltage by 90 degrees

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E5B10 (A)

What is the relationship between the AC current through an inductor and the voltage across an inductor?

A. Voltage leads current by 90 degrees

B. Current leads voltage by 90 degrees

C. Voltage and current are 180 degrees out of phase

D. Voltage and current are in phase

~~

**Impedance (Z)**

The impedance of a circuit is the combined values of the resistance and reactances XL and XC. Since XL is +j and Xc is -j, they partially cancel each other. At the resonant frequency, they are equal and the resulting impedance is just resistance and in phase. If they are not equal, the impedance is the resistance plus the residual XL or XC, whichever was the greater quantity. The resulting phase angle is a vector somewhere between +90 and 0 for inductive circuits and -90 and 0 for capacitive circuits. If the resistive and reactive component are equal, the resulting phase is 45 degrees. These figures are for positive values of resistance.