# Careful Measurement of Emf and or Internal Resistance of a Cell

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• Published : January 9, 2013

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Careful measurement of emf and or internal resistance of a cell Aim
To measure voltage and current in the circuit and from that figure work out emf and internal resistance of the cell, to identify errors involved and deal with them in the most effective way and maintain a safe working environment at all times. Background

EMF (electromotive force) is a measure of work done per unit of charge and is measured in volts. Internal resistance is resistance in ohms of the cell. I will be using a 1.5V battery in the experiment. I will measure the voltage and current using multimeters. Calculation method

I intend to rearrange the equation ‘ε=Ir+IR’ to form ‘V= -Ir +ε’ and then draw the y=mx+c graph equation to find EMF and internal resistanc`e. The y axis intercept measures EMF and the gradient gives you internal resistance. Projected main sources of error

The multimeter has some inaccuracies: Resistance is accurate to 0.1 ohms (+/-0.8%), Current is accurate to 0.03 A (+/- 2%) and voltage is accurate to 1 mV (+/- 0.5%). These on their own are minor problems but may have a cumulative affect. The resistance of all the wires joined together is 0.6 ohms. But the biggest uncertainty after early testing is the fluctuations on the ammeter, the ammeter very rarely settles on a value which leads to an inaccuracy of 0.02 volts (+/- 0.01 volts) and 0.02 amps (+/- 0.01 amps). This uncertainty could be very high especially with lower values First experiment

I started with a simple experiment to get figures from which improvements could be achieved.

This is the circuit diagram of my first experiment

It was soon clear that the variable resistor didn’t have the necessary resistance to induce the current necessary for the experiment. I replaced the original variable resistor with a rheostat as the resistance could be changed in a more linear way rather than with the exponential increases of the variable resistor. There are few safety hazards in my experiment but to be sure I made sure there was no copper showing in wires, only touched the rheostat when it wasn’t connected to the cell and was wary of dangers associated with being near other experiments.

Current (A)| Uncertainty (A)| Voltage (V)| Uncertainty (V)| 0.23 | +/- 0.01| 1.439| +/- 0.01|
0.29 | +/- 0.01| 1.425| +/- 0.01|
0.31| +/- 0.01| 1.421| +/- 0.01|
0.33| +/- 0.01| 1.415| +/- 0.01|
0.36| +/- 0.01| 1.408| +/- 0.01|
0.41| +/- 0.01| 1.398| +/- 0.01|
0.45| +/- 0.01| 1.388| +/- 0.01|
0.52| +/- 0.01| 1.372| +/- 0.01|
0.58| +/- 0.01| 1.359| +/- 0.01|
0.68| +/- 0.01| 1.339| +/- 0.01|
0.78| +/- 0.01| 1.317| +/- 0.01|
0.91| +/- 0.01| 1.299| +/- 0.01|
My initial results and graph (on next page):

My initial results were very encouraging as the correlation was very strong. I repeated the same experiment but taking more time.
These results form a clear negative correlation. However at the end of the experiment, the results went away from the line of best fit sharply showing there was a mistake that clearly occurred during the experiment. I originally thought this was a problem with the battery heating up over time so decided to measure resistance of rheostat in my next experiment so the battery would have a time to cool down. Current (A)| Uncertainty (A)| Voltage (V)| Uncertainty (V)| 0.74| +/- 0.1| 1.286| +/- 0.1|

0.48| +/- 0.1| 1.354| +/- 0.1|
0.36| +/- 0.1| 1.375| +/- 0.1|
0.29| +/- 0.1| 1.396| +/- 0.1|
0.23| +/- 0.1| 1.400| +/- 0.1|
0.20| +/- 0.1| 1.392| +/- 0.1|

See atatched graph (next page)

I also measured the voltage from my battery in between experiments and discovered my ‘1.5V’ battery to be producing 1.559V, a percentage error of 4%. To try and rectify this problem I tried new batteries until one with a very low percentage error was found, one with 1.503V which had negligible error.

Second experiment
As my initial first experiment brought back...