**Alternating Current Circuits**

The difference between Direct Current

**(D.C.)**and Alternating Current**(A.C.)**is that current in a D.C. circuit does not vary and only flows in one direction. D.C. circuits are at their peak value (+) or at their zero point (0) and do not vary in between. They could be compared to a light switch that is either completely on, or off.**Direct Current (D.C.)**

A.C. circuits flow in two directions. Alternating first from negative to positive, then positive to negative. An

**A.C.**circuit starts at a zero point

**(0)**, gradually reaches a maximum

**(+)**peak value, then drops gradually past the zero point

**(0)**until reaching

**(-)**peak, then gradually completes the cycle by returning to zero. In the United States electricity is generated normally at 60 of these cycles (hertz) per second.

**Alternating Current (A.C.)**

Because of its uniqueness an

**A.C.**circuit voltage has to be measured differently. Peak voltage of a typical**A.C.**circuit is approximately 170 volts. But, it’s only at that maximum point for a brief moment, most of the time the voltage is somewhere between 0 and 170. The Code defines voltage as the “greatest root-mean square difference of potential.” This is commonly referred to as the “effective voltage” which is about**70.7%**of the measured peak voltage, or in this case 170 x .707 = 120 volts. We commonly use “effective voltage” as a measurement of voltage on all circuits.**A.C. Resistance**

When

This works fine if all we want to do is turn on an incandescent light bulb or cook food on a broiler. But, what if we want to ring a doorbell, use a motor, or a transformer. These devices require coils which cause electrical energy to be converted into mechanical energy in the form of work. A common term we use for a coil of wire is an inductor.

**A.C.**or**D.C.**current flows through a type of resistor, like a heating element, electrical energy is converted to heat. In fact, all of the ohms law formulas can be used to express wattage, voltage and amps in simple resistance circuits.This works fine if all we want to do is turn on an incandescent light bulb or cook food on a broiler. But, what if we want to ring a doorbell, use a motor, or a transformer. These devices require coils which cause electrical energy to be converted into mechanical energy in the form of work. A common term we use for a coil of wire is an inductor.

Inductors

An inductor is coil of wire in a circuit which first causes a build up then a delay in the release of current in a circuit. Even though inductance is a physical characteristic of a conductor wound into a coil it is often defined in terms of its effect on the flow of current.

*Inductance is defined as that property of an electric circuit that tends to oppose any change*

of current through a circuit.of current through a circuit.

As currents rise in a coil, the magnetic field around the conductor produces a counter voltage that opposes the current flow causing it to rise slowly before being released. This type of opposition to current flow causes current to lag behind voltage producing a type of resistance called inductive-reactance

Although there are drawbacks to using inductors in a circuit they are, for the most part, very useful devices. When a coil (inductor) is looped around a metal post it's called an electromagnet. This can be useful in picking up large metal objects or ringing a doorbell. Transformers use mutual induction to transfer electricity from one coil of wire to another coil of wire through one common iron core at different voltages and ampacities. Motors and generators induce magnetic fields through coils to produce mechanical motion. Inductance is measured in henrys

**(XL).**Although there are drawbacks to using inductors in a circuit they are, for the most part, very useful devices. When a coil (inductor) is looped around a metal post it's called an electromagnet. This can be useful in picking up large metal objects or ringing a doorbell. Transformers use mutual induction to transfer electricity from one coil of wire to another coil of wire through one common iron core at different voltages and ampacities. Motors and generators induce magnetic fields through coils to produce mechanical motion. Inductance is measured in henrys

**(L)**.Capacitors

**Capacitors or Condensers (C) are used in an electrical circuit to store and then release a voltage, or difference of potential.**Some circuits require capacitors to accomplish work.They are used in electric discharge lighting to attain a high voltage 60 cycle pulse which ignites a gas in the fluorescent bulb. They are also used in air-conditioners as booster starters. A capacitor is made up of two conductive plates with an insulative material in between. A potential builds in the conductive plates while separated until a peak voltage is reached. Then, either the voltage automatically breaks through the barrier or the charge is released through a mechanical switch. In either case voltages much higher than normally available are attained for short periods of time. Capacitor circuit voltage tends to lag behind its current causing a type of resistance called capacitive-reactance

**(XC)**. You may have experienced reactance in a circuit when you get a sudden annoying buzzing noise when you turn on a fluorescent light while listening to the radio. Capacitance is measured in farads**(C)**.Impedance

The difference between a resistive circuit and an inductive, or capacitive, circuit is that the circuit changes when a voltage is applied. In an inductive circuit the voltage leads and current lags behind. In a capacitive circuit current leads and voltage lags behind.

This is best remembered in the saying

This is best remembered in the saying

**"ELI the ICE man"**where old ELI stands for...

*Voltage (E) leads, in Inductance (L), the Current (I)*And what ELI does for a living, he's the ICE man...

*Current (I) leads, in Capacitance (C), the Voltage (E).***Impedance (Z)**, on the other hand, is the total opposition to current flow of an AC circuit. This includes the Inductive-Reactance

**(XL),**Capacitive-Reactance

**(XC)**, and Resistance

**(R)**of a circuit.

Impedance, in this case

**“Z”**is normally measured in ohms and can be expressed in the

**following formula for a circuit containing resistance, inductance, and capacitance...**

For a circuit containing resistance and inductance...

For a circuit containing resistance and capacitance...

For a circuit containing only resistance...

Z = R

For a circuit containing only inductance...

Z = XL

For a circuit containing only capacitance...

**Z = XC**

Formulas for voltage, current, and impedance...

**E = I x Z**

**I = E**/ Z

**Z =**

**E**

**/ I**

**Example:**Calculate the Impedance (Z) of a circuit with the following.....

R = 30

L = 20

C = 10

L = 20

C = 10

Phase Angle

In

same time.

**D.C.**circuits resistance**(R)**and voltage**(E)**are in phase. In other words, they both reach their peaks and zero points at thesame time.

In

**A.C.**circuits voltages and currents have both magnitude and direction. Inductive- reactance**(XL)**and capacitive-reactance**(XC)**are measured in ohms but their directions are opposite. Inductive-reactance**(XL)**lags resistance by 90 ̊ while capacitive-reactance**(XC)**leads resistance by 90 degrees.Inductance produces opposition to the flow of current and also makes current lag behind voltage in a circuit. In a purely inductive circuit (one without resistance) the current would lag the voltage by 90 degrees (1/4 cycle) behind the voltage. The term that we commonly use for this is “out of phase.” In actual circuits containing resistance and inductance the current will lag, or be out of phase, between 0 and 90 degrees behind the voltage. The angle of lag of a current in an inductive circuit can be calculated from this formula...

**Tangent Of Angle Of Lag =**

**XL**

**/ R**

Capacitance produces opposition to voltage and tends to make it lag behind the current of a circuit. In a purely capacitive circuit (one without resistance) the voltage would lag the current by 90 degrees (1/4 cycle) behind the current. The term that we commonly use for this is “out of phase.” In actual circuits containing resistance and capacitance the voltage will lag, or be out of phase, 0 to 90 degrees behind the current. The angle of lag of a current in a capacitive circuit can be calculated from this formula...

**Tangent Of Angle Of Lag =**

**XC**

**/ R**

Cosine Of The Angle

Cosines for different angles is the trigonomic equivalent of what’s called “Power Factor.” The symbol

The phase angle of a circuit containing resistance, inductance, and capacitance can be found using the following formula...

**Ø**, the Greek letter theta, is often used to designate the angle of lag, or lead of a circuit. Hence power factor is sometimes referred to a**cosine Ø**(cosine theta) meaning the cosine of the**angle Ø.**The phase angle of a circuit containing resistance, inductance, and capacitance can be found using the following formula...

**Cosine Of The Phase Angle (Power Factor) = R /**

**Z**

Wasted internal work presents itself as heat and thus reduces the work performed by a discharge light or motor. The loss due to this wasted work can be expressed by this formula...

Where (

In industrial plants a low power factor is usually due to underloaded induction motors because the power factor of motors is much less at partial loads than at full loads. This can be corrected by installing smaller motors, capacitive discharge lighting, or by installing capacitor banks to offset the inductive effects of motors.

**W)**= the loss in watts,**(I)**= the current in amps on the conductor, and**(R)**= the resistance in ohms. It requires much larger equipment and conductors to deliver the a certain amount of power at a low power factor than at a high power factor (close to 1).In industrial plants a low power factor is usually due to underloaded induction motors because the power factor of motors is much less at partial loads than at full loads. This can be corrected by installing smaller motors, capacitive discharge lighting, or by installing capacitor banks to offset the inductive effects of motors.

Power Factor

Power in an A.C. circuit is, as we have learned, is voltage times current

**(W = E x I)**when only resistance is available. When inductance and capacitance is available we have to take it into account. To do that we include Power Factor in the formula...**W = E x I x PF**

Power factor is the ratio of watts, commonly called

Here’s the formulas commonly used to find power factor, watts, and volt-amps...

**“true power”**to the volt-amps**(vA)**, commonly called**“apparent power”**of an**A.C.**circuit. True power is what is actually consumed in a circuit. Apparent power is what is available in the circuit. We usually express this difference as a percentage, or decimal point. In other words, a power factor of .8 (or 80%). Thus, a power factor of .8 means that the current and voltage is out of phase, meaning that only 80% of the wattage will be available. Or, there will be a 20% loss in wattage in the circuit. The highest power factor possible is 1, or 100%. Wattmeters are used to measure real power.Here’s the formulas commonly used to find power factor, watts, and volt-amps...

**Power Factor =**

__Watts__**Volt-Amps**

**Watts =**

**Volt-Amps x Power Factor**

**Volt-Amps =**

__Watts__**Power Factor**

**Types Of Power Factor Loads**

Here’s a simplified way of determining the Power Factor (P.F.) formulas above...

Just put your thumb on the value you are looking for.

**Example #1:**How much power is consumed in a circuit which operates at 115 volts, draws 8 amperes and has a power factor of 80% ?**Solution,,,****Watts = Volt-Amps x Power Factor**

**Watts = 115 volts x 8 amps (W=E x I) x .**

**8 (80%)**

**Watts = 736**

**Example #2:**Measurements were taken in an A.C. circuit and the current flowing was 20 amps, 120 volts, and 2500 watts. What is the power factor of this circuit ?

**Power Factor =**

__Watts__**Volt-Amps**

**Power Factor =**

__1____20__

__v x 20__

__a__**2500w**

**Power Factor = .96 (96%)**