AGH University of Science and
Technology in Cracow
Department of Electronics
Laboratory Manual
Physics_1
Title:
Experiment
No.
Maximum Power Transfer
2009 r.
5
1. Goal
To measure current and voltage difference across the load. To find effective power in function
of load. To establish conditions of maximum power transfer in a circuit..
2. What to learn?
Electric potential. Potential difference. Power in electric circuits. Electromotive force (emf).
Ideal emf device. Real emf device. Kirchhoff's voltage law. Kirchhoff's current law. Current
in a single-loop circuit. Internal resistance. Power of
emf device. Dissipation power.
Matching load to the power source – maximum power transfer in a circuit.
3. Background
A power supply can be represented by an ideal voltage source of ε volts in series with an
internal resistance r (Fig. 1).
Fig. 1. Real electromotive force (emf) source loaded with the external resistor R
Let’s express the power Pdiss dissipated in the resistor R as a function of R and then find where
this function has its maximum. The power Pdiss dissipated in a resistor R is given by the
2
formula P = I R, where I is the current flowing through the resistor. Expressing the current I
as a function of R (using Ohm's law) gives:
I=
ε
R+r
Now we can express the power P as a function of R:
Pdiss = ε 2
R
( R + r )2
Now calculate the derivative dPdiss/dR:
dPdiss
r−R
=ε2
dR
( R + r )2
This derivative is equal to zero when R = r. For this value of resistance R , the power Pdiss is a
maximum. The emf device produces power Pemf = ε ⋅ I . The power efficiency η for this
circuit is equal to:
η=
Pdiss
.
Pemf
4. Equipment
Power supply (emf source ε ) of high internal resistance r. DC voltmeter. DC ammeter.
External potentiometer. Switch on/off.
5. Measurements
1. Set up the circuit given in Fig. 2:
Fig. 2. Measurement set-up
2. Set the voltmeter to the mode DC, range 20V. Set the ammeter to the mode DC, range
200 mA.
3. Set the potentiometer R to the maximum value of resistance.
4. Switch the circuit on. Measure the I-U characteristics for the entire available range of
parameters U and I. Fill in the Table 1.
Table 1.
I [A]
U[V]
R[Ω]
Pdiss [W]
Pemf [W]
ε [V]
r[Ω]
η[%]
R/r
4. Data Handling
1. Calculate the load resistance R and power dissipated in this load Pdiss and complete
the Table 1.
2. Draw the plot U=f(I).
3. Find the equation of the regression line that fits the data. Find the regression
coefficients a and b and uncertainties of these coefficients Δa and Δb .
4. Using the Kirchhoff's voltage law for the single-loop circuit shown in Fig. 1, find the
potential difference across the resistor R: U= -r I+ ε.
(**)
5. By comparing the coefficients of the regression line and the coefficients of the
equation describing potential difference across the external resistor (**) find the
electromotive force ε and inertial resistivity r of this source .
6. Establish uncertainties the electromotive force Δε and inertial resistivity Δr.
7. Calculate the total power produced by the emf source Pemf and the efficiency η.
8. Plot graphs of Pdiss, Pemf, η against the ratio R/r and on their basis come to conclusion
when the maximum power is transferred in a circuit. What is the efficiency in this
case?
Literature:
1. Halliday, Resnick “Fundamentals of Physics - 8th edition”, John Wiley 2007,
2. Zięba “Pracownia Fizyczna Wydziału Fizyki I Techniki Jądrowej AGH”, Uczelniane
Wydawnictwo Naukowo-Dydaktyczne 1999.
Updated: 14.02.2009 by Barbara Dziurdzia