As we said last month, electrical theory underlies everything we do in the electrical construction business. It is therefore necessary to review this theory regularly. We continue now, with Ohm's Law.

### OHM'S LAW

From last month's explanation of the three primary electrical forces, we see the relationships that they have to each another. (More voltage, more current; less resistance, more current.) These relationships are calculated by using what is called Ohm's Law.

Ohm's Law states the relationships between voltage, current and resistance. The law states that in a DC circuit, current is directly proportional to voltage and inversely proportional to resistance. Accordingly, the amount of voltage is equal to the amount of current multiplied by the amount of resistance. Ohm's Law goes on to say that current is equal to voltage divided by resistance and that resistance is equal to voltage divided by current.

In an AC circuit, current equals voltage divided by impedance.

These three formulas are shown in Fig. 1, along with a diagram, which helps in remembering Ohm's law. This Ohm's law circle can be used to obtain all three of these formulas easily. The method is this: Place your finger over the value that you want to find (E for voltage, I for current, or R for resistance), and then the other two will make up the formula. For example, if you place your finger over the E in the circle, the remainder of the circle will show **I × R.** If you then multiply the current times the resistance, you will get the value for voltage in the circuit. If you wanted to find the value for current, you would put your finger over the I in the circle, and then the remainder of the circle will show **E**/**R**. So, to find current we divide voltage by resistance. Lastly, if you place your finger over the R in the circle, the remaining part of the circle shows **E**/**I**. These Ohm's law formulas apply to any electrical circuit, no matter how simple or how complex.

If you remember only one electrical formula, make sure it's Ohm's law. This Ohm's law circle makes remembering the formula simple.

By using the example of a water system, we can compare the relationship explained by Ohm's law to a very small pipe or a large pipe. If you have a water pressure on your system of 10 lbs per sq in., for example, you can expect that a large volume of water would flow through a 6-in. diameter pipe. Through a ½-in. pipe, however, a much smaller amount of water would flow. We would say that the ½-in. pipe had a much higher resistance to the flow of water than did the 6-in. pipe. Similarly, a circuit with a resistance of 10 ohms (resistance is measured in ohms) would let twice as much current flow as a circuit which had a resistance of 20 ohms. Likewise, a circuit with 4 ohms would allow only half as much current to flow as a circuit with a resistance of 2 ohms.

### KIRCHOFF'S LAWS

The most important and basic laws of circuits are *Kirchoff's laws*.

### Voltage

Kirchoff's voltage law states that the sum of the voltage rises minus the sum of voltage drops around a series circuit will equal zero. In other words, the sum of all voltages in a series circuit equal zero. This means that the voltage of the source will be equal to the total of voltage drops (which are of opposite polarity) in the circuit. In simple and practical terms, the sum of voltage drops in the circuit will always equal the voltage of the source. In a parallel circuits or parallel branches, the voltages across parallel elements are equal.

### Current

Kirchoff's second law, applied to series circuits, is really just common sense — that the sum of currents entering and exiting a node equals zero; that current is the same in all parts of the circuit. It is fairly obvious that if the circuit has only one path, what flows through one part will flow through all parts. In a parallel circuit, the currents split so that the voltages are equal. Where parallel circuits begin and end, the sum of the currents must be zero.

### WATTS

Another important electrical term is watts. Watts are the conversion of electricity into heat, but the watt can also be used as the basic measurement of electrical power; a measurement of the amount of work performed. For instance, 1 hp equals 746W; 1 kW (the measurement the power companies use on our bills) equals 1,000W.

The most commonly used formula for power (or watts) is voltage times current (**E × I**). For example, if a certain circuit had a voltage of 40V with 4A of current flowing through the circuit, the wattage of that circuit would be 160W (40 × 4). Fig. 2 on page 24R shows the 12 power formulas that can be formed by combining both Ohm's law and Watt's law.

Please note that the paragraph above uses common terms, and is more than adequate for power wiring and associated applications. To be completely correct, E × I is VA (volt amps), not watts.

### REAL POWER VERSUS APPARENT POWER

One of the more difficult concepts in the electrical industry is the difference between *real power* (also called *true power*) and *apparent power*. We will cover this briefly.

*Real* (or *true*) *power* is the actual power used in an electrical circuit. Real power is expressed in watts (W).

*Apparent power* is the product of voltage and current in a circuit, measured without considering any phase variance between voltage and current in the circuit. It is expressed in volt amps (VA).

*Real power* is always less than apparent power in reactive circuits. The ratio of real power to apparent power is called the *power factor*. A perfect power factor (where there was no difference between real and apparent power) would be 1.0, which is called *unity*. Typical power factors for industrial buildings would be 0.9 or less.

Apparent power is the power that you can measure with a typical voltmeter and ammeter. The technical definition is: The measure of alternating current power that is computed by multiplying RMS (root-mean-square) voltage and RMS current. This is called apparent power, because it is the power that is measured by the most common means — the power that appears to you.

Real power is more complex. In a purely resistive circuit (with no reactance), apparent power is the same as true power. But when voltage and current move out of phase with each other, things get complicated. To measure real power, the waveform must be divided into many segments, and a large number of voltage and current readings must be taken and then averaged. Specialized watt meters and reactive power meters are designed to do this.