Download Load Resistance, Internal Resistance and Power Dissipation

Load Resistance, Internal Resistance and Power Dissipation
Introduction
No battery or power supply can deliver an infinite amount of power. If we apply a short
circuit across the terminals of a battery, Ohm’s law might lead us to expect that the current
drawn from the battery would be infinite, since R is zero. We often model the fact that a battery
cannot deliver an infinite amount of power by representing an actual battery as composed of an
emf Ɛ in series with an internal resistance Ri. In this lab you develop a method for determining
the value of the internal resistance Ri and the ideal internal battery Ɛ by using a voltmeter and
applying Ohm’s law.
Theory
The circuit that you use is shown in Figure 1. A load resistor RL and a voltmeter are
connected to the power source shown. The power PL dissipated in the load is given by
PL = I2RL
(1)
In Equation (1) I is the current flowing through the load resistor.
We may apply Ohm’s law and write Equation (1) in terms of the voltage drop across the load VL.
PL = VL2/RL
(2)
Procedure
The power source consists of a AA battery in series with a resistor which will act at the
internal resistance. This Ri resistor is covered in black or silver tape. It is needed because the
internal resistance of the battery alone is around an ohm. Measuring such a small resistance
usually means drawing a substantial amount of current from the battery. The internal resistance
has a value between several tens of ohms to a few hundred ohms. The battery and the black or
silver resistor together constitute the power supply.
Construct the circuit shown in Figure 1. Use the Ri with the black tape. There are seven
load resistors, RL, to measure. Record the voltage for each.
From your data, calculate the current through each load resistor. Calculate the power
dissipated in each load resistor.
By hand, graph the dissipated power (mW) vs. the load resistance (Ω). The line of best fit
will be a curve. The peak of the curve indicates maximum power.
Perform the same experiment with the silver Ri resistor. Plot your data on same graph.
Analysis
The physical application of this lab is impedance matching which is used for technology
such as speakers and antennas. Maximum power is achieved when RL = Ri. Using your graph,
find the Ri that provides maximum power.
You can also calculate Ri. Using your black Ri data table, pick a V1 and corresponding
RL1. Also pick a V2 and corresponding RL2. Now, use the formula:
R𝑖
𝑉 2 – 𝑉1
=
(
𝑉1
𝑉
− 2)
𝑅𝐿1 𝑅𝐿2
(3)
Compare the calculated Ri to the one you found graphically. Repeat this for the silver Ri.
Next, find Ɛ. Using your black Ri data table, pick an I and corresponding RL. Use your calculated
(not graphically found) Ri. Now, use the formula:
Ɛ = I Ri + I R L
Compare the calculated Ɛ to the expected value.
Conclusion
In your lab report, be sure to include your black and silver Ri (found graphically and
calculated) and Ɛ (calculated).
Comment on which Ri gives the bigger power curve.