ETCAI formulas

## ETCAI formulas

ETCAI (Electrical & Electronics Technology Computer Aided Instruction) is a computer program made by C. E. Ormon and ETCAI Products which aims to teach electrical and electronic engineering concepts. It's not a particularly ingenious program, but it's one of the best-known programs for this purpose, simply because it doesn't have a lot of competition. The company behind it has a homepage at www.etcai.com, but their website only advertises newer, Windows-based products which each cover specific areas of EE (DC, AC, digital, etc.) instead of the broader coverage given by the original MS-DOS based ETCAI program (which covered all these fields). The DOS version, then, appears to be abandonware; You can still find it at several websites if you search for a file called ETCAI.ZIP.

ETCAI consists mostly of using some established math formulas and using them to fill in some blanks. These formulas are standardized and well-known within EE, but if you're a student you might not know all of them. Thus, this page intends to tell you the formulas you need to know to answer ETCAI's tests. This page is divided according to each type of test contained in the program.

Note that not all of the test types have been placed here yet. I'm starting with the AC circuit calculations (which tend to be the most difficult), and later on I intend to add the DC ones. If you can understand AC, however, you should find DC to be considerably simpler to analyze and do calculations with.

## RL Series Circuits

An RL (Resistor-Inductor) series circuit in ETCAI is simply a resistor in series with an inductor, connected to an AC power source.

XL is inductive reactance. It is calculated in the normal way, using the standard formula for inductive reactance, namely:

```2 * pi * f * L
```

...Where pi is the math constant pi (3.14...), f is the frequency of the AC power source, and L is the inductance of the inductor.

Z is impedance, calculated using the following formula:

```sqrt( (R^2) + (X^2) )
```

q is the Greek letter Theta. In this context, it refers to the phase angle of the circuit. It's calculated using this formula:

```invtan (XL / R)
```

It (total current), IR (current going through the resistor), and IL (current going through the inductor) will all be the same, because this is a series circuit. Only in parallel circuits will the currents be different. In this case, all of these will be the AC source voltage divided by Z, then multiplied by 1,000. This is because current is voltage divided by impedance (I = E / Z), and the program measures the current in milliamps (mA), not amps (A), so you need to multiply by 1,000 to get the correct answer.

ER is the energy (voltage) across the resistor. It is the current through the resistor (IR) times the actual resistor's resistance. (E = IR)

EL is the energy (voltage) across the inductor. It is the current through the inductor (IL) times the inductive reactance (XL).

Pa is apparent power. It's the current (It) times the voltage of the AC power source. In general, current times voltage equals power.

Pt is true power. The reason why "apparent" power is not the actual power is that much of the apparent power used by this circuit is actually reactance. The inductor is not actually using any power in this circuit, but it appears to, because of its reactance. In reality, however, when the direction of the AC current inverts during each cycle, the inductor gives back the energy it absorbed, so it's not actually wasting any power. Thus, true power will be only the power used by the resistor, which really is using up power. Pt, then, is IR times ER, because current times voltage equals power.

## RC Series Circuits

An RC (Resistor-Capacitor) series circuit in ETCAI is a resistor in series with a capacitor, connected to an AC power source. Don't confuse this kind of RC circuit with a Radio Control circuit, which is also abbreviated RC.

XC is capacitive reactance, calculated using the following standard formula:

```        1
XC = --------
2*pi*f*C
```

Z is impedance, calculated using the following formula:

```sqrt( (R^2) + (X^2) )
```

q is the Greek letter Theta. In this context, it refers to the phase angle of the circuit. It's calculated using this formula:

```invtan (XC / R)
```

It (total current), IR (current going through the resistor), and IC (current going through the capacitor) will all be the same, because this is a series circuit. Only in parallel circuits will the currents be different. In this case, all of these will be the AC source voltage divided by Z, then multiplied by 1,000. This is because current is voltage divided by impedance (I = E / Z), and the program measures the current in milliamps (mA), not amps (A), so you need to multiply by 1,000 to get the correct answer.

ER is the energy (voltage) across the resistor. It is the current through the resistor (IR) times the actual resistor's resistance. (E = IR)

EC is the energy (voltage) across the capacitor. It is the current through the capacitor (IC) times the capacitive reactance (XC).

Pa is apparent power. It's the current (It) times the voltage of the AC power source. In general, current times voltage equals power.

Pt is true power. The reason why "apparent" power is not the actual power is that much of the apparent power used by this circuit is actually reactance. The capacitor is not actually using any power in this circuit, but it appears to, because of its reactance. In reality, however, when the direction of the AC current inverts during each cycle, the capacitor gives back the energy it absorbed, so it's not actually wasting any power. Thus, true power will be only the power used by the resistor, which really is using up power. Pt, then, is IR times ER, because current times voltage equals power.

## RLC Series Circuits

An RLC (Resistor-Inductor-Capacitor) series circuit in ETCAI is a resistor, an inductor, and a capacitor, all connected in series to an AC power source.

XC is capacitive reactance, calculated using the following standard formula:

```        1
XC = --------
2*pi*f*C
```

XL is inductive reactance. It is calculated in the normal way, using the standard formula for inductive reactance, namely:

```2 * pi * f * L
```

After you've calculated these two reactances, you'll need to stop for a moment and calculate the total reactance (X) of the circuit. Although this is not actually an answer you'll need to fill in, you'll still need to know it before answering the next question. When reactance is plotted graphically, inductive reactance (XL) is graphed upward, and capacitive reactance (XC) is graphed downward. Mathematically, XL is considered positive, and XC is considered negative. Thus, X = XL - XC.

Z is impedance, calculated using the following formula:

```sqrt( (R^2) + (X^2) )
```

q is the Greek letter Theta. In this context, it refers to the phase angle of the circuit. It's calculated using this formula:

```invtan (X / R)
```

It (total current), IR (current going through the resistor), IC (current going through the capacitor), and IL (current going through the inductor) will all be the same, because this is a series circuit. Only in parallel circuits will the currents be different. In this case, all of these will be the AC source voltage divided by Z, then multiplied by 1,000. This is because current is voltage divided by impedance (I = E / Z), and the program measures the current in milliamps (mA), not amps (A), so you need to multiply by 1,000 to get the correct answer.

ER is the energy (voltage) across the resistor. It is the current through the resistor (IR) times the actual resistor's resistance. (E = IR)

EC is the energy (voltage) across the capacitor. It is the current through the capacitor (IC) times the capacitive reactance (XC).

EL is the energy (voltage) across the inductor. It is the current through the inductor (IL) times the inductive reactance (XL).

Pa is apparent power. It's the current (It) times the voltage of the AC power source. In general, current times voltage equals power.

Pt is true power. The reason why "apparent" power is not the actual power is that much of the apparent power used by this circuit is actually reactance. The inductor and capacitor are not actually using any power in this circuit, but they appear to, because of their reactance. In reality, however, when the direction of the AC current inverts during each cycle, the inductor and capacitor give back the energy they absorbed, so they're not actually wasting any power. Thus, true power will be only the power used by the resistor, which really is using up power. Pt, then, is IR times ER, because current times voltage equals power.

## RLC Parallel Circuits

An RLC (Resistor-Inductor-Capacitor) parallel circuit in ETCAI is a resistor, an inductor, and a capacitor, all connected in parallel to an AC power source.

XC is capacitive reactance, calculated using the following standard formula:

```        1
XC = --------
2*pi*f*C
```

XL is inductive reactance. It is calculated in the normal way, using the standard formula for inductive reactance, namely:

```2 * pi * f * L
```

Z is impedance. It will be the AC source voltage divided by It, the total current. This is because Z = E/I, impedance equals voltage divided by current. You'll notice that this is a different formula from the other AC circuits in ETCAI. This is because we're working with a parallel circuit, not a series circuit. Although the Z = E/I rule applies in series circuits too, it's not very useful there, because we need to know Z to calculate E and I, so we can't calculate them until Z is known. In parallel circuits, however, determining E and I is not dependant on knowing Z.

q is the Greek letter Theta. In this context, it refers to the phase angle of the circuit. It's also calculated using a different formula than the series AC circuits:

```invtan ( (IC - IL) / IR)
```

It is sqrt ( (IR^2) + ( (IL-IC)^2 )

IR is the current through the resistor. It will be the AC source voltage divided by the resistor's resistance. (I = E/R)

IC is the current through the capacitor. It will be the AC source voltage divided by XC, the capacitive reactance.

IL is the current through the inductor. It will be the AC source voltage divided by XL, the inductive reactance.

ER, EC, and EL will all be the same. They will all be simply the AC source voltage. In a parallel circuit, all branch circuits are simply the source voltage.

Pa is apparent power. It's the current (It) times the voltage of the AC power source. In general, current times voltage equals power.

Pt is true power. The reason why "apparent" power is not the actual power is that much of the apparent power used by this circuit is actually reactance. The inductor and capacitor are not actually using any power in this circuit, but they appear to, because of their reactance. In reality, however, when the direction of the AC current inverts during each cycle, the inductor and capacitor give back the energy they absorbed, so they're not actually wasting any power. Thus, true power will be only the power used by the resistor, which really is using up power. Pt, then, is IR times ER, because current times voltage equals power.

Back to the electronics section

Back to the main page