AReS

PART1R, L, C Circuit

Experiment 9 :Maximum Power Conversion Theory

Theory

Using Thevenin’s equivalent circuit, DC power can be considered as a circuit in which the battery V and internal resistance r are connected in series as in fig. below. To use the power from this power source, the load resistance RL should be connected as in fig.1-14.

fig1-14

Fig. 1-14Maximum Power Conversion

Here, the power delivered to the load P_L changes according to the value of load resistance R_L, so let’s find out the value of R_L that makes P as maximum.

$P_L` (R_L ) ~=~ I^2` R_L ~=~ ( V over {R`+`R_L})^2 R_L``$
(1)

To find out the maximum value of P_L, if P_L is differentiated to R_L and put as 0,

$dP_L over dR_L ~=~ V^2 over {(R`+`R_L )^3} (R-R_L ) ~=~ 0``$
(2)

Therefore,

R_L ~=~ R``
(3)

That is, if the load resistance becomes same as internal resistance, the power delivered to the load resistance becomes maximum, and here, the value of maximum power delivered to the load resistance is

$P_{L,max} ~=~ P_L` (R_L = R ) ~=~ V^2 over 4R ``$
(4)

Like this, when the value of load resistance satisfies the condition of maximum power delivery, the circuit is said to become impedance matched. Meanwhile, the total power supplied by the power source, that is, the sum of power PT consumed at internal resistance R and load resistance R_L is

$P_T ~=~ V^2 over {R``+``R_L }``$
(5)

As R_L increases, P_T does monotone decreasing. Idea power source is the case when the internal resistance R is 0, and here, P_L = P_T does monotone decreasing as R_L increases.

Experiment Process

fig1-15

Fig. 1-15Experiment Circuit of Maximum Power Conversion

1. In the circuit as in fig.1-15, measure the current flowing to VR1.

Measure by turning the variable resistance to the left end, and turn it gradually to the right and measure the current at the location same as the value of table 1-9 and record the result in the relevant column of table 1-9.

2. Calculate the power value of this circuit. (P = I² x R)

3. Repeat the experiment above by changing the value of variable resistance VR1 as in table 1-9 and complete the table.

tab1

Experiment 1-9.1 In Block a of M01, compose a circuit as in fig.1-15.

1.Connection(M01 Module)

1.Connect the measuring module(ARES-EI-M01) to the platform.

2.Circuit Connection

Connect 1, 2 terminals of VR1 on the left of Block a with yellow lines.

Connect terminal 1 of VR1 on the left of Block a to the left terminal of VR1 with yellow line, and terminal 3 to the right terminal with yellow line.

3.Power Connection

Connect between +15V terminal of Fixed Power and the left terminal of R1 of Block a with red line, and between GND terminal and the left terminal of VR1 with black line.

4.Measuring Instrument Connection

Connect between mA/A of Multimeter and the right terminal of R1 with red line, and between Low terminal and the right terminal of VR1 with black line.

2.Wiring Diagram

flash

3.Current Measurement

1If you click dmm at left menu, Digital Multimeter window appears, and if you click dci , the current value is indicated.
2How to Measure the Resistance of VR1
To measure the resistance, the power should be cut off from the circuit. Therefore, pull out the line connected between mA/A terminal and right terminal of R1 and connect it between High terminal and the left terminal of VR1.

When you choose the connected ohm at Digital Multimeter screen, the resistance value is measured. Set up as the relevant column of table 1-9 and measure and record the current.

To measure the current at the setup resistance value, pull out the line connected between High terminal of Multimeter and the left terminal of VR1 and connect it between mA/A terminal and the right terminal of R1.

⑤ Calculate the power value of this circuit. (P = I² x R)
Power(P) = W

⑥ Repeat the experiment above by changing the value of variable resistance as the table below using the multimeter, and complete the table.

Experiment Result Report

result
Title	Maximum Power Conversion Theory	Date
Department		Id Number		Name

1. Experiment Result Table

Table 1-9

result_table
Resistance [㏀]	0	0.5	1	1.5	2	2.5	3	4	4.5	5
Measured Value of Current [mA]
Calculated Value of Current [mA]
Calculated Value of Power[mW]

2. Review and Explanation

1) Using table 1-9, draw a characteristic curve in the graph below.

section paper