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Experiment2

Single Phase AC Circuits

Objectives: - To apply single phase AC circuit using lab-volt device in the lab practically and

simulation using (LVVL) program.

- Draw the phasor diagram of the circuits and display output on oscilloscope window.

Theory:

An AC circuit consists of a combination of circuit elements and a power source The power

source provides an alternative voltage, The output of an AC power source is sinusoidal and

varies with time according to the following equation :Δv = ΔVmax sin (ωt).

But ,why study AC circuits? You probably live in a house or apartment with sockets that

deliver AC. Your radio, television and portable phone receive it, using (among others) circuits

like those below. As for the computer you're using to read this, its signals are not ordinary

sinusoidal AC, but, thanks to Fourier's theorem, any varying signal may be analyzed in terms of

its sinusoidal components. So AC signals are almost everywhere. And you can't escape them,

because even the electrical circuits in your brain use capacitors and resistors.

Before examining the driven RLC circuits, let’s first consider the simple cases where only one

circuit element (a resistor, an inductor or a capacitor) is connected to a sinusoidal voltage source.

Table1 Purely load circuits

Purely Resistive load Purely Inductive Load Purely Capacitive Load

(t) and ( )are in phase

with each other.

The current lags voltage by

π/2 in an inductive circuit.

The current leads the voltage

by π/2 in a capacitive circuit

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Each of the following circutes will be identified and analyzed:

Part 1// Series AC Circuits

RL Series Circuit:

A circuit that contains a pure resistance R ohms connected in series with a coil having pure

inductance of L (Henry) is known as RL Series Circuit. The circuit diagram of RL Series Circuit is

shown below:

Figure 1 Series RL Circuit and its Phasor diagram

,,,, ,,,,

√( ) ( )

√( ) ( )

From the phasor diagram shown above it is clear that the current in the circuit lags the applied

voltage by an angle and this angle is called the phase angle.

=

=

power factor = cos( )

AC Circuits

Series

RL RC RLC

Parallel

RL RC RLC

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RC Series Circuit:

A circuit that contains pure resistance R ohms connected in series with a pure capacitor of

capacitance C farads is known as RC Series Circuit. A sinusoidal voltage is applied to and

current I flows through the resistance (R) and the capacitance (C) of the circuit. The RC Series

circuit is shown in the figure below:

Figure 2 Series RC Circuit and its Phasor diagram

,,,, ,,,,

√( ) ( )

√( ) ( )

From the phasor diagram shown above it is clear that the current in the circuit leads the applied

voltage by an angle ϕ and this angle is called the phase angle.

=

=

power factor = cos( )

RLC Series Circuit:

The RLC Series Circuit is defined as when a pure resistance of R ohms, a pure inductance of L

Henry and a pure capacitance of C farads are connected together in series combination with each

other. As all the three elements are connected in series so, the current flowing in each element of

the circuit will be same as the total current I flowing in the circuit. The circuit diagram of RLC

Series Circuit is shown below:

Figure 3 Series RLC Circuit

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The phasor diagram of the RLC Series Circuit when the circuit is acting as an inductive circuit

that means (VL>VC) is shown below and if (VL< VC) the circuit will behave as a capacitive

circuit.

Figure 4 Phasor diagram for series RLC Circuit

√( ) ( )

√( ) ( ) = I Z

From the phasor diagram, the value of phase angle will be:

( )

,,,,

There are three cases of RLC Series Circuit:

When XL > XC, the phase angle ϕ is positive. The circuit behaves as a RL series circuit in

which the current lags behind the applied voltage and the power factor is lagging.

When XL < XC, the phase angle ϕ is negative, and the circuit acts as a series RC circuit in

which the current leads the voltage by 90 degrees.

When XL = XC, the phase angle ϕ is zero, as a result, the circuit behaves like a purely

resistive circuit. In this type of circuit, the current and voltage are in phase with each other.

The value of power factor is unity. The current value will be as high as possible. The value of

resistance is minimal.

Figure 5 Relationship between impedance and current with frequency when XL=XC

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Part 2//Parallel AC Circuits

Parallel RL circuit

Since the resistor and inductor are connected in parallel, the input voltage is equal to

output voltage but the currents flowing in resistor and inductor are different. The parallel RL

circuit is not used as filter for voltages because in this circuit, the output voltage is equal to

input voltage and for this reason it is not commonly used as compared to series RL circuit. The

circuit diagram of RL Parallel Circuit is shown below:

Figure 6 Parallel RL Circuit and its Phasor diagram

,,,,

,,,,

√( ) ( )

From the phasor diagram, the value of phase angle will be:

=

=

power factor = cos( )

Parallel RC circuit

A resistor–capacitor circuit (RC circuit), or RC filter , is an electric circuit composed

of resistors and capacitors driven by a voltage or current source. A first order RC circuit is

composed of one resistor and one capacitor and is the simplest type of RC circuit.

RC circuits can be used to filter a signal by blocking certain frequencies and passing others. The

two most common RC filters are the high-pass filters and low-pass filters; band-pass

filters and band-stop filters usually require RLC filters, though crude ones can be made with RC

filters.

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The circuit diagram of RC Parallel Circuit is shown below:

Figure 7 Parallel RC Circuit and its Phasor diagram

,,,,

,,,,

√( ) ( )

From the phasor diagram, the value of phase angle will be:

=

=

power factor = cos( )

Parallel RLC circuit

RLC Parallel circuit is the circuit in which all the components are connected in parallel across

the alternating current source. In contrast to the RLC series circuit, the voltage drop across each

component is common and that’s why it is treated as a reference for phasor diagrams. The circuit

diagram of RLC Parallel Circuit is shown below:

Figure 8 Parallel RLC Circuit and its Phasor diagram

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The phasor diagram of the RLC Parallel Circuit when the circuit is acting as a capacitive circuit

that means (IL>IC) is shown below and if (IL< IC) the circuit will behave as an inductive circuit.

Figure 9 Phasor diagram for parallel RLC Circuit

√( ) ( )

√( ) ( )

=

From the phasor diagram, the value of phase angle will be:

( )

,,,,

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Experimental Procedures:

Part1//RL Series circuit

(Note: Only one circuit will be explained in detail)

1- Ensure that the power supply is switched off. Then Connect the circuit by (LVVL)

program as shown in figure 10.

2- Switch on the switch in the resistive load to get the resistor value 2200Ω.

3- Switch on the switch in the resistive load to get the inductor value 7H.

4- Switch on the power then use the indicator to set input voltage at 110V(by put the

voltage control Knob 50%).

Figure 10 Series RL Circuit

5- Open the metering window to reading the values of E1, E2, E3 and I1 as shown in figure

below (V= 115.7v ,, VR=76.46v ,, VL=77.16v ,, I=0.035A)

Figure 11: Metering window at 50% voltage source

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6- Open phasor window to display the phasor diagram of the circuit and choose the

reference current I1 as shown in figure12.

Figure 12 phasor window

7- Open oscilloscope window to display the AC output signal in resistor and inductor as

shown figure below.

Figure 13 Oscilloscope windows

Channel 1

Input. . . . . ……. . . . E1

Sensitivity . . . . 50 V/div

Input Coupling . . . . . DC

Channel 2

Input. . . . . . . . . . . . . . E2

Sensitivity . . . . . 50 V/div

Input Coupling. . . . . . DC

Channel 3

Input .. . . ………... . . . E3

Sensitivity. . . ….. 50 V/div

Input Coupling ….. . . . DC

Channel 4

Input . . . …………….. . . I1

Sensitivity . . . . . 0.02 A/div

Input Coupling .. . . …. . DC

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Part2// Make (RC series, RLC series, RL parallel ,RC Parallel ,RLC Parallel) at different values

of loads and to achieve a good analysis of the circuit.

Exercise

Find all values of voltages and currents in these circuits by (LVVL) program and theoretically,

then draw the phasor diagram foe each circuit.

a) Vin = 50V ,, F=50Hz

b) Vin = 150V ,, F=50Hz

Useful information:

In (LVVL) program, you can find power factor, phase angle by click the right mouse button and on

metering window and go to metering settings)