# F2-1: Determination of the Internal Resistance of a Cell Using a Potentiometer¶

## Apparatus¶

Leclanché Cell (filled to bottom of paint line with saturated Ammonium Chloride solution); metre bridge board; \(3\text{V}\) battery (fresh cells); jockey; switch; galvanometer with \(100\Omega\) series resistor; rheostat (\(\sim 15 \Omega\) resistance); resistors values: \(5\Omega\), \(10\Omega\), and \(20\Omega\); block with crocodile clips (for resistor); connecting leads (3 long, 7 short); 1 sheet graph paper.

## Procedure¶

- Construct the above circuit, with \(R =\infty\Omega\). Close the
switch
**S**. After placing**J**\(5\text{cm}\) from**B**, adjust the rheostat until the galvanometer reads zero (balance point). Note the length \(l_{\infty} = \overline{AJ}\). Open**S**. - Connect \(R = 30\Omega\), Close
**S**, and find the balance point. Read \(l = \overline{AJ}\). Repeat with \(R = 25, 20, 15, 10, \text{and } 5\Omega\). Tabulate \(R\) and \(l\). Open**S**.

*NOTE: After the experiment, empty the Ammonium Sulphate solution out of
the cell again, to ensure a maximum lifetime for the solution.*

## Theory¶

Consider the lower branch of the circuit when the galvanometer reads zero. It is effectively disconnected from the top branch of the circuit:

Therefore:

And therefore:

However the length \(l\) is proportional to the potential difference \(V\), and when \(R=\infty\Omega\), \(V = E\). Thus let \(V = kl\) and \(E = kl_{\infty}\),where \(k\) is a constant. Therefore:

And therefore:

## Analysis¶

- Plot a graph of \(\frac{1}{R}\) vs. \(\frac{1}{l}\) and find the gradient.
- Use the gradient, the value of \(l_{\infty}\), and the last equation in the theory only to find the internal resistance of the cell, \(r\).

## Questions¶

- In the theory why can we say that the lower branch is ‘effectively disconnected’ from the top branch of the circuit?
- If the resistance of wire
**AB**is \(2\Omega\) and its length is \(100\text{cm}\), find an expression for \(k\) in terms of \(V_{AB}\) only.

- Compare the Leclancé Cell and the modern Dry Cell. List a) the similarities and b) the differences.
- Define a) internal resistance and b) electromotive force. Thus explain carefully why in the theory, when \(R =\infty \Omega\), then \(V = E\).