Synopsis on Measuring Internal Resistance of a Cell

Internal resistance is the barrier to current flow supplied by the cells and batteries themselves, resulting in heat creation. Ohms are used for measuring internal resistance. The relation between electromotive force (e) and internal resistance (r) in cells is represented by:

e = I (r + R)

Where e is the electromotive force (Volts), R is the load resistance, I is the current (A) and r is the cell’s internal resistance in ohms.

When we rearrange the equation above, we get:

e = IR + Ir or,

e = V + Ir

V is the potential difference (terminal) across the cell when the current (I) flows through the circuit in the above equation.

Potentiometer of a cell

A potentiometer is a device used to measure a cell’s internal resistance, compare the emf of two cells and determine the potential difference throughout a resistor. It is made up of a long wire with a consistent cross-sectional area and a length of 10 metres. 

Wire material should be high resistive and have a low-temperature coefficient. On a wooden board, the wires are extended parallel to each other. Thick copper strips are used to connect the wires in series. On the wooden board, there is also a metre scale.

It is based on the idea that when current flows consistently through a wire with a uniform cross-sectional area, the potential difference between two points is proportional to the wire’s length.

EMF equation

The maximum potential difference between two electrodes of a cell is known as emf (electromotive force).

Dynamic-induced emf is generated when a current-carrying conductor cuts the magnetic flux using relative motion. The magnitude of induced emf is directly proportional to the negative variation rate of the magnetic flux attached to the circuit.

As chemical energy is turned into electrical energy, the emf of a cell decreases as current is extracted from it. The correct way to measure is to do it in such a way that no current is pulled from the cell to achieve accurate emf. Because this isn’t practical, the measurement is done under conditions when the current pulled from the cell is so little that it’s almost undetectable. Poggendorff first articulated the principle of the procedure, which is today known as the Poggendorff compensating method.

The uncertain emf of a cell is contrasted by a cell with a known emf in this procedure. Therefore, it’s called the “compensating method”. Volt is the unit of measurement. A potentiometer circuit is the type of electrical circuit employed.

An anode is an electrode that undergoes oxidation, while a cathode is an electrode that undergoes reduction. A metal develops potential in relation to the electrolyte when it comes into contact with its own ion solution. 

AB is a wire with constant resistance. Through a variable resistance, R, the wire’s ends A and B are attached to two electrodes of a lead storage battery C. There is a progressive drop in potential through the wire AB proportional to its length. 

One of the cell’s electrodes, E, whose emf measurement is to be done, is connected to A via a galvanometer, G. The other electrode is connected to AB by a sliding contact D via a key, K. The emf of the cell is the potential difference between both the anode and cathode.

The contact D is moved along the wire after pressing the key K to the point that there is no deviation from the galvanometer, thus indicating no current flow.  The potential drop across the wire AB from point A to D is equivalent to cell E’s potential. When cell E is replaced by a standard cell with a highly precise potential, a new position of the contact D is discovered when the flow of current through the galvanometer is zero. 

At this position:

Length of the wire cell / Length of the wire with cell S

= Potential of the cell E / Potential of the cell S

The cell’s potential, E, may be calculated using the known value of the standard cell’s potential, S and the experimentally established value of the wire lengths.

Alternatively, the trial of the cell could be read directly using a high resistance voltmeter linked to the two electrodes of the two half-cells. A high resistance voltmeter enables only a little amount of current to pass and has little effect on electrolyte concentrations.

A device known as a potentiometer is used to take actual measurements. The basic premise is the same as before, but rather than a length of wire, there are two circular resistances, R1 and R2, which are directly calibrated in volts.

Conclusion

A cell’s electromotive force is always higher than the potential difference between adjacent cells. The internal resistance of a cell is thus determined by elements such as the length between the electrodes, the effective area of the electrodes, the temperature and the solution concentration. Thus, while solving questions, if you know the formula, 

e = I (r + R), 

then you can easily solve it depending on the given values of each component.