Question

Why do we prefer a potentiometer to measure the emf of a cell rather than a voltmeter?

Answer 1

The primary reason we prefer a potentiometer to measure the EMF of a cell is that a potentiometer draws no current from the cell at the point of measurement. A voltmeter, by its very nature, must draw some current to operate.

Let's break this down in detail.

1. The Difference Between EMF and Terminal Voltage

First, it's crucial to understand the difference between a cell's EMF (Electromotive Force) and its Terminal Voltage.

• EMF (E): This is the maximum potential difference a cell can provide. It's the voltage across its terminals when no current is flowing. Think of it as the cell's total, ideal voltage.
• Terminal Voltage (V): This is the actual potential difference across the cell's terminals when it is supplying current to a circuit.

Every real cell has some internal resistance (r). When current (I) flows from the cell, there is a voltage drop inside the cell itself, equal to Ir. This "lost voltage" reduces the voltage available to the external circuit.

The relationship is given by the equation:

V = E - Ir

• V is the Terminal Voltage (what you measure when the circuit is running)
• E is the EMF (the true, maximum voltage)
• I is the current flowing
• r is the internal resistance

2. How a Voltmeter Works (The Problem)

A voltmeter is connected in parallel across the component whose voltage you want to measure. For a voltmeter to work (whether it's a digital display or a moving coil), it must draw a small amount of current from the circuit.

• When you connect a voltmeter across a cell, it draws a current (let's call it $I_v$).
• Because this current $I_v$ is flowing, there will be a voltage drop across the cell's internal resistance, equal to $I_v \cdot r$.
• Therefore, the voltmeter does not measure the true EMF (E). It measures the terminal voltage: $V = E - I_v \cdot r$.

Even for a very good voltmeter with high resistance, $I_v$ is small but not zero. So, the reading on the voltmeter will always be slightly less than the true EMF of the cell. This is sometimes called the "loading effect."

3. How a Potentiometer Works (The Solution)

A potentiometer is a much more clever device. It works on the null deflection principle.

• A potentiometer sets up a known potential gradient along a wire using a separate driver circuit.
• The cell whose EMF you want to measure (the test cell) is connected to this wire through a galvanometer (a very sensitive current detector).
• You move a sliding contact (jockey) along the wire until you find a point where the potential difference on the wire is exactly equal and opposite to the EMF of the test cell.
• At this "balance point," the galvanometer shows zero current (null deflection).

Since no current (I = 0) is being drawn from the test cell at the moment of measurement, the internal voltage drop term (Ir) becomes zero.

*V = E - (0 r) => V = E**

Therefore, the potentiometer measures the true EMF of the cell, unaffected by its internal resistance.

---

Summary Table

| Feature | Potentiometer | Voltmeter |
| :--- | :--- | :--- |
| Working Principle | Null Deflection Method (balancing voltages) | Deflection Method (based on current flow) |
| Current Drawn | Zero current is drawn from the cell at the balance point. | Draws a small current from the cell to operate. |
| What it Measures | The true EMF (E) of the cell. | The Terminal Potential Difference (V). |
| Accuracy for EMF | Highly accurate. It is the standard method for calibrating other voltmeters. | Less accurate. The reading is always slightly lower than the true EMF. |
| Effect of Internal Resistance | The measurement is independent of the cell's internal resistance. | The measurement is affected by the cell's internal resistance. |
| Ideal Counterpart | It acts as an ideal voltmeter (which has infinite resistance). | It is a practical, non-ideal voltmeter. |
| Convenience | Bulky, requires setup, and is not a direct reading instrument. | Portable, easy to use, and gives a direct reading. |

Conclusion

While a voltmeter is far more convenient for general-purpose measurements in a circuit, a potentiometer is the preferred instrument for accurately measuring the EMF of a source because its null-deflection method ensures no current is drawn, thereby eliminating any error caused by the source's internal resistance.