AReS

PART3AC Circuit

EXperiment 3 :RC & RL Circuit

Theory

(1) The AC resistance of the capacitor is X_C=-1/(2π fÇ) and X_C gets lower as the frequency of AC flowing on the capacitor gets higher. All condensers of this feature has not only AC resistance but also DC resistance which delays the energy charge and resistance loss which discharges the charged energy. Therefore, if the AC resistance of the capacitor is X_C and the DC resistance is R, the combined resistance is impedance and it is indicated as Z. The relationship between the current and the voltage follows Ohm’s law and the impedance Z and the phase are expressed as below.

Z=R-jX_C, Z=E/I, Φ=tan^(-1) 〖-X〗_C/R

fig3-10

Fig. 3-10R-C Circuit and Phase

Fig. 3-10 shows R-C series circuit. The combined resistance (impedance) of R-C circuit becomes
Z=√(R²+X_C²). And the phase difference of the voltage to the current becomes not 90° but as in Fig. 3-10 (b).

(2) The AC resistance X_L of the inductor has 90° phase difference between the current and the voltage. However, if the DC resistance R is included in series in the coil, the combined resistance(impedance) can be expressed as the formula below and the relationship between the voltage and the current follows Ohm’s law.

Z=R+jX_L, Z=E/I, Φ=tan^(-1) X_L/R

fig3-11

Fig. 3-11Relationship of R-L Circuit and Phase

Fig. 3-11 shows R-L series circuit and the combined resistance(impedance) becomes Z=√(R²+X_L²). And when DC resistance R exists in the circuit, the phase difference of the voltage to the current becomes not 90° but as in Fig. 3-11(b). In the circuit that has no AC resistance(Reactance), the calculation of the power load is P=IE. However AC circuit is different from the load that has DC resistance only because of the phase angle of the voltage and the current. The ratio of .impedance Z and R is called power factor and it is expressed as PF=R/Z=cosΦ. Here, the power to R load is called effective power and the power to Z is called apparent power, and they are expressed as below.

PF= (Effective Power)/(Apparent Power) =cosΦ

Experiment Process

RC Circuit

fig3-12

Fig. 3-12C-R Circuit and Impedance(Z)

tab1

Experiment 3-3.1 RC Circuit (Compose as in Fig. 3-12 (a))

1.Connection

1.Circuit Connection

Function Generator Conenction

Connect between A+ terminal of Signal Output on the front panel and 3a terminal of Circuit-3 with red line, and between A- terminal and 3e terminal of Circuit-3 with black line.

Voltmeter Connection

Connect between A+ terminal of Signal Output CH A on the front panel and 3a terminal of Circuit-3 with red line, and between A- terminal and 3b terminal of Circuit-3 with black line.

Connect between B+ terminal of Signal Output CH B on the front panel and 3b terminal of Circuit-3 with red line, and between B- terminal and 3c terminal of Circuit-3 with black line.

2.Wiring Diagram

flash

3.Measurement

1Choose analog output at the left menu of front panel.
In Function Generator window, choose Amplitude as 10v , Frequency as 1kand Signal as sine , and click on to output 1KHz 10V p-p.
2Choose analog input at the left menu of front panel.
Choose Volt & Ampere Meter and choose voltage , rms , ac at CH A and CH B each, then the measured value is indicated. Record it in the Relevant Frequency column. Ch A is Ec, and CH B is ER
3Choose analog output at the left menu of front panel.
In Function Generator window, choose Amplitude as 10v , Frequency as 100and click arrow to make frequency 500hz and execute process 2).

In Function Generator window, Amplitude as 10v , Frequency as 100 and click arrow to make 1500Hz frequency 1.5khz and execute process 2).

In Function Generator window, Amplitude as 10v , Frequency as 1k and click arrow to make 2000Hz frequency 2.0khz and execute process 2).
4Connect the red line between A+ terminal of Signal Input CH A and 3a terminal of Circuit-3 to 3d terminal, and the black line between A- terminal and 3b terminal of Circuit-3 to 3e terminal.
5Choose analog input at the left menu of front panel and choose Volt & Ampere Meter, then the measured value of CH A is Eo. Record it in table 3-3.

4.Calculation

1. Calculate impedance Z with the given formula and record it in table 3-3

RL Circuit

fig3-13

Fig. 3-13Relationship of L-C Circuit and Phase

tab2

Experiment 3-3.2 RL Circuit (Compose as Fig. 3-13 (a))

1.Connection

1.Circuit Connect

Function Generator Connection

Connect between A+ terminal of Signal Output on the front panel and 3i terminal of Circuit-3 with red line, and between A- terminal and 3j terminal of Circuit-3 with black line.

Voltmeter Connection

Connect between A+ terminal of Signal Output CH A on the front panel and 3f terminal of Circuit-3 with red line, and between A- terminal and 3g terminal of Circuit-3 with black line.

Connect between B+ terminal of Signal Output CH B on the front panel and 3g terminal of Circuit-3 with red line, and between B- terminal and 3h terminal of Circuit-3 with black line.

2.Wiring Diagram

flash

3.Measurement

1Choose analog input at the left menu of front panel.
In Function Generator window, choose Amplitude as 10v, Frequency as 1k and Signal as sine , and click on to output 1KHz 10V p-p.
2Choose analog inputat the left menu of front panel
Choose Volt & Ampere Meter and choose voltage , rms , ac at CH A and CH B each, then the measured value is indicated. Record it in the relevant Frequency column of table 3-4. Ch A is EL, and CH B is EC
3Choose analog output at the left menu of front panel
In Function Generator window, choose Amplitude as 10v , Frequency as 100and click arrow to make frequency 500hz and execute process 2).

In Function Generator window, choose Amplitude as 10v , Frequency as 100and click arrow to make frequency 1.5khz and execute process 2).

In Function Generator window, choose Amplitude as 10v , Frequency as 1kand click arrow to make frequency 2.0khz and execute process 2).
4Connect the red line between A+ terminal of Signal Input CH A and 3f terminal of Circuit-3 to 3i terminal, and the black line between A- terminal and 3g terminal of Circuit-3 to 3j terminal.
5Choose analog input at the left menu of front panel and choose Volt & Ampere Meter, then the measured value of CH A is Eo. Record it in table 3-3

4.Calculation

1. Calculate impedance Z with the given formula and record it in table 3-4.

Experiment Result Report

result
Title	RC & RL Circuit	Date
Department		Id Number		Name

1. Experiment Result Table

2. Review and Explanation

1) Calculate X_C for each frequency, and calculate the impedance according to the Z formula and calculate the voltage of the capacitor’s both ends and that of the resistance’s both ends using Ohm’s law.

2) Calculate X_L for each frequency, and calculate the impedance according to the Z formula and calculate the voltage of the coil’s both ends and that of the resistance’s both ends using Ohm’s law.

Frequency	E_O	E_C	E_R	Z=√(R²+X²_C )
500 ㎐
1000 ㎐
1500 ㎐
2000 ㎐

Frequency	E_O	E_L	E_R	Z=√(R²+X²_L )
500 ㎐
1000 ㎐
1500 ㎐
2000 ㎐

PART3AC Circuit

EXperiment 3 :RC & RL Circuit

Theory

Experiment Process

RC Circuit

Experiment 3-3.1 RC Circuit (Compose as in Fig. 3-12 (a))

1.Connection

1.Circuit Connection

2.Wiring Diagram

flash

3.Measurement

4.Calculation

Experiment 3-3.2 RL Circuit (Compose as Fig. 3-13 (a))

1.Connection

1.Circuit Connect

2.Wiring Diagram

flash

3.Measurement

4.Calculation

Experiment Result Report

1. Experiment Result Table

2. Review and Explanation

1) Calculate X_C for each frequency, and calculate the impedance according to the Z formula and calculate the voltage of the capacitor’s both ends and that of the resistance’s both ends using Ohm’s law.

2) Calculate X_L for each frequency, and calculate the impedance according to the Z formula and calculate the voltage of the coil’s both ends and that of the resistance’s both ends using Ohm’s law.

3) Compare the calculated value and the measured value.

3. Discuss the experiment result.

PART3AC Circuit

EXperiment 3 :RC & RL Circuit

Theory

Experiment Process

RC Circuit

Experiment 3-3.1 RC Circuit (Compose as in Fig. 3-12 (a))

1.Connection

1.Circuit Connection

2.Wiring Diagram

flash

3.Measurement

4.Calculation

Experiment 3-3.2 RL Circuit (Compose as Fig. 3-13 (a))

1.Connection

1.Circuit Connect

2.Wiring Diagram

flash

3.Measurement

4.Calculation

Experiment Result Report

1. Experiment Result Table

2. Review and Explanation

1) Calculate XC for each frequency, and calculate the impedance according to the Z formula and calculate the voltage of the capacitor’s both ends and that of the resistance’s both ends using Ohm’s law.

2) Calculate XL for each frequency, and calculate the impedance according to the Z formula and calculate the voltage of the coil’s both ends and that of the resistance’s both ends using Ohm’s law.

3) Compare the calculated value and the measured value.

3. Discuss the experiment result.

1) Calculate X_C for each frequency, and calculate the impedance according to the Z formula and calculate the voltage of the capacitor’s both ends and that of the resistance’s both ends using Ohm’s law.

2) Calculate X_L for each frequency, and calculate the impedance according to the Z formula and calculate the voltage of the coil’s both ends and that of the resistance’s both ends using Ohm’s law.