Describe the use of voltmeters (analogue and digital) with different ranges

4.2.3 Electromotive Force and Potential Difference

Learning Objective

Describe how analogue and digital voltmeters are used, including range selection, internal resistance, correct parallel connection, safety limits, and how to record and analyse measurements.

Key Definitions

• Electromotive force (EMF, E) – the maximum potential difference a source can supply when no current flows (open‑circuit).
  

  Formula: \(E = \dfrac{W}{Q}\) where \(W\) is the electrical work done on a charge \(Q\). Unit: volt (V).
  

  Note: EMF is the work done by the source in moving a unit charge round a complete circuit.

• Potential difference (PD, V) – the work done per unit charge when the charge moves between two points of a component.
  

  For a source the PD measured across its terminals while it delivers current is called the terminal voltage and is lower than the EMF because of the source’s internal resistance \(r\).
  

  Formula: \(V = E - I r\) or, for any component carrying current, \(V = \dfrac{W}{Q}\). Unit: volt (V).

• Voltmeter – an instrument that measures the potential difference between two points. It must always be connected in parallel with the component whose voltage is required.

Analogue vs Digital Voltmeters

General Procedure for Using a Voltmeter

1. Select the appropriate range – choose the smallest range that is just above the expected voltage. This gives the best resolution.
2. Connect the meter in parallel** with the component:

   • Red (positive) lead to the point at higher potential.
   • Black (negative) lead to the point at lower potential.

3. Never connect in series. A series connection forces the meter to carry the circuit current, gives a false (usually much lower) reading and may damage the instrument.
4. Power the meter and allow a few seconds for the needle or display to stabilise after any range change.
5. Read the voltage:

   • Analogue – note the needle position and estimate to the nearest 0.1 division.
   • Digital – read the numeric value directly; note the least‑count (e.g., 0.01 V).

6. If the display shows “OL” (over‑load) the voltage exceeds the selected range – switch to a higher range.

Safety & Precautions

• Never exceed the instrument’s maximum voltage rating (usually 250 V). Over‑voltage can damage the meter or cause a safety hazard.
• Use the lowest possible range for low voltages to improve resolution.
• For analogue meters view the needle straight on to avoid parallax error.
• Observe correct polarity; reversing the leads gives a negative reading.
• When measuring a live circuit keep hands away from exposed conductors and use insulated leads.

Recording Measurements & Estimating Uncertainty

1. Record:

   • Instrument type (analogue or digital) and range used.
   • Reading (to the appropriate number of significant figures).
   • Estimated uncertainty:

     • Analogue – ±½ of the smallest scale division.
     • Digital – ±1 least‑count digit (add the % accuracy if required).

2. Use the recorded values to calculate any derived quantities (e.g., EMF, internal resistance) and propagate uncertainties where required.

Practical Example – Determining the EMF and Internal Resistance of a Cell

Goal: Find the EMF (\(E\)) and internal resistance (\(r\)) of a 1.5 V dry cell.

Calculations

1. Current through each load: \(I = \dfrac{V_{\text{load}}}{R}\)

   • For 10 Ω: \(I_1 = \dfrac{1.20}{10} = 0.120\; \text{A}\)
   • For 20 Ω: \(I_2 = \dfrac{1.30}{20} = 0.065\; \text{A}\)

2. Apply the terminal‑voltage equation \(V = E - I r\) to each load:

   
   \(1.20 = E - 0.120 r\) (1)

   
   \(1.30 = E - 0.065 r\) (2)

   
   Subtract (2) from (1): \(-0.10 = -0.055 r\) → \(r = \dfrac{0.10}{0.055} \approx 1.8\;Ω\)

3. Substitute \(r\) back into (1): \(E = 1.20 + 0.120 \times 1.8 \approx 1.416\; \text{V}\)
4. Uncertainty (simplified): combine the voltage uncertainties (±0.01 V) to give roughly ±0.02 V for \(E\) and ±0.2 Ω for \(r\).

The open‑circuit voltage (1.498 V) is close to the calculated EMF (≈1.42 V); the small difference is due to measurement uncertainties and the assumption of a constant internal resistance.

Summary

• EMF is the open‑circuit voltage of a source; terminal PD falls when current flows because of internal resistance.
• Voltmeters must always be connected in parallel with the component of interest.
• Analogue meters: manual range, lower internal resistance, needle reading – higher chance of loading low‑voltage circuits.
• Digital meters: manual or auto‑range, very high internal resistance, numeric read‑out – higher accuracy and negligible loading.
• Select the smallest suitable range, respect the maximum voltage rating, record readings with appropriate uncertainties, and use the data to calculate EMF, internal resistance, or other derived quantities.