1. What a Potentiometer Is
A potentiometer is a device used to measure EMF and potential difference accurately. It works by comparing an unknown EMF with a known voltage using a long uniform wire. Instead of drawing current from the cell under test, it balances it against a known potential drop, giving very precise results.
A key idea is that measurement is based on null deflection, meaning no current flows through the galvanometer when the balance point is reached.
2. Principle of the Potentiometer
The potentiometer is based on the principle that the potential drop across a uniform wire is directly proportional to its length, provided the current in the wire remains constant.
2.1. Potential Gradient
The potential drop per unit length of the wire is called the potential gradient.
\( k = \dfrac{V}{L} \)
Where:
- k = potential gradient
- V = total voltage applied across the wire
- L = total length of the wire
2.1.1. Meaning of Potential Gradient
If the wire is uniform, each centimetre has the same resistance. So each equal segment drops the same voltage. This makes the potentiometer extremely accurate.
3. Working of the Potentiometer
To use the potentiometer, the unknown EMF is connected in a secondary circuit along with a galvanometer and a sliding contact (jockey). The jockey is moved along the wire until the galvanometer shows zero deflection.
This point is called the null point.
3.1. Null Point Condition
At the null point, the potential difference across the length \( l \) of the potentiometer wire equals the EMF being measured.
\( E_X = k l \)
4. Measuring EMF Using the Potentiometer
The unknown EMF is found by balancing it against a known potential gradient. Once the null point is located, the EMF is simply:
\( E_X = k l \)
4.1. Interpretation
If the potentiometer wire is 100 cm long and the null point appears at 40 cm, and the potential gradient is, say, 0.02 V/cm, then the EMF is:
\( E_X = 0.02 \times 40 = 0.8\,\text{V} \)
5. Comparing Two EMFs
The potentiometer can compare two cells without drawing any current from them, making the comparison very accurate.
5.1. Formula for Comparison
If two cells give null points at lengths \( l_1 \) and \( l_2 \), then:
\( \dfrac{E_1}{E_2} = \dfrac{l_1}{l_2} \)
5.1.1. Meaning
The longer the balancing length, the larger the EMF. The ratio of EMFs is directly equal to the ratio of null-point lengths.
6. Measuring Internal Resistance of a Cell
The potentiometer can also be used to measure internal resistance by comparing EMF with terminal voltage when the cell is delivering current through a known external resistor.
6.1. Steps for Internal Resistance Measurement
- First, find EMF \( E \) by keeping the cell open.
- Then connect a known resistance \( R \) across the cell.
- Find the terminal voltage \( V \) using the potentiometer again.
The internal resistance is then:
\( r = R \left( \dfrac{E - V}{V} \right) \)
7. Why the Potentiometer Is Very Accurate
The potentiometer works by balancing, not by drawing current from the source being measured. This means the reading is unaffected by internal resistance or loading effects. As long as the wire is uniform and current remains constant, the potentiometer gives extremely precise results.
8. Simple Way to Visualise It
Imagine a ruler with perfectly equal markings. If you want to measure some length precisely, you match it to the ruler without bending or stretching it. The potentiometer does exactly this electrically—it compares unknown voltages against a uniform voltage drop along a wire.