Internal Resistance

Internal Resistance of Cells

Does the fact that a 9v battery has 6 cells create a higher internal resistance than a AA battery with 1 cell?

Activities

Determine Internal Resistance of Cell
Energy within a circuit.

Resources

EMF- Hyperphysics Focus on the portion described by batteries and energy within a cell. The production through a magnetic field will be describe in the next unit.

Problems

To measure the internal resistance of a battery the PD across the terminals needs to be measured as current flows, in this practical the current is varied by changing the length of a piece of nichrome resistance wire connected across the terminals.

Theory

The circuit can be represented by the diagram below, where:

R represents the resistance wire
ε the electromotive force of the battery
r the internal resistance of the battery
I is the current in the circuit

The equation for this circuit is ε = IR + Ir (Energy provided by the battery is 'used' by the resistor (R) and internal resistance (r). The internal resistance is in series with the rest of the circuit.

Rearranging this gives (Create a graph to show this relationship)

R = ε/I - r

Alternatively we can write, (Create a graph to show this relationship)

IR = -Ir + ε

Connect the circuit shown in the diagram.
Connect the LabQuest to your computer with Vernier Graphical Analysis Running.
Insert the Ammeter into the circuit and connect the Ammeter to the LabQuest.
Connect the voltmeter over the variable resistor, connect it to the LabQuest.
By rotating the variable resistor, you will see the values of the ammeter and voltmeter changing.
Use the mode of SELECTED EVENTS. Your choice to use average over 10 sec.
Change the axis of your graph to x-axis: Current and y-axis: Voltage
Press Collect (Green Button). For each of the 10 values on the variable resistor, press KEEP.
Press STOP. Graphical Analysis will automatically store your data.
Change to a different batter setup.
Estimate the uncertainties in each measurement and enter into the headers of the table.

Analysis (complete BOTH)

Method 1:

According the the theory R = ε/I - r so a graph of R vs 1/I should be a straight line with gradient ε and intercept -r. Calculate values of 1/I in your spreadsheet (create a calculated column) then plot the relevant graph to find ε and r.

Method 2:

The equation can also be written as: IR = -Ir + ε where IR = V, the PD across the resistance wire (also equal to the PD across the terminals of the battery). Plot a graph of V vs I to find ε and r.

Conclusion and evaluation

Compare the values obtained for each method. Which method gave the best value for each quantity?

What effect did the meters have on your measurements?

Sample data.

Possible further explorations:

investigate different types of battery
explore other uses of the meter bridge
heating effect of a battery
effect of temperature on internal resistance
relationship between age of battery and EMF and internal resistance
relationship between EMF and r and concentration of acid in a simple cell
relationship between EMF and r and dimensions and material of plates in a simple cell
EMF and r of a lemon battery
use simulation to investigate effect of wire resistance on results

Current Flow

Discharging a battery (cell), the electrons flow through the resistor while the protons flow across the 'salt-bridge'.

Identifying the direction of current flow required to recharge a cell

The two GIFs indicate the direction of electron flow while discharging (left) and REcharging a battery.

Recharging a battery (cell), requires the protons to be 'driven/forced' across the salt-bridge. The movement of protons across the bridge requires work be done on the system.

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