Scientific investigation in physics follows a systematic approach that involves:

• Observation – identifying phenomena and asking research questions
• Hypothesis – formulating testable predictions
• Experimentation – designing and carrying out controlled experiments
• Data collection – using appropriate instruments to measure quantities
• Data analysis – processing and interpreting measurements
• Conclusion – drawing findings based on evidence

Accurate measurement is fundamental to all experimental physics. The choice of instrument and proper measurement technique directly affects the reliability of results.

Common Instruments

Proper Usage Guidelines

1. Ammeter: Connect in series; ensure positive terminal joins positive terminal of source
2. Voltmeter: Connect in parallel across component being measured
3. Multimeter: Select correct function and range before measurement
4. Zero error: Always check and adjust for zero error before taking readings

Example 2.1: Measuring resistance using voltmeter and ammeter

A student connects a resistor in series with an ammeter and a 6 V battery. The voltmeter connected across the resistor reads 4.2 V, and the ammeter reads 0.14 A. Calculate the resistance.

Solution:

Using Ohm's law: $R = \frac{V}{I}$

$R = \frac{4.2 \text{ V}}{0.14 \text{ A}} = 30 \Omega$

The resistance is 30 Ω.

Common Instruments

Usage Notes

• Hall probe must be properly calibrated before use
• The probe should be positioned perpendicular to magnetic field lines
• Zero adjustment is necessary before measuring weak magnetic fields

Common Instruments

CRO Usage

1. Adjust focus and brightness controls
2. Set appropriate timebase (time/div)
3. Select appropriate voltage scale (volts/div)
4. Connect probe to the test point
5. Observe and sketch the waveform

Common Instruments

Common Instruments

Example 2.2: Measuring Solar Panel Efficiency

A student investigates a solar panel by measuring output voltage at different tilt angles. The data obtained:

From this data, the student observes that maximum voltage (24.1 V) occurs at 40° tilt angle. This demonstrates how tilt angle affects solar panel performance.

Common Instruments

Safety Note

When using radiation instruments:

• Always wear appropriate protective equipment
• Follow safety protocols strictly
• Never expose yourself or others to unnecessary radiation

Common Instruments

Example 2.3: Measuring Radioactive Decay

A student uses a Geiger-Müller counter to measure radiation from a radioactive sample. The count rates recorded over time:

The decreasing count rate demonstrates radioactive decay. The student can use this data to determine the half-life of the radioactive material.

Before Measurement

• Identify the quantity to be measured
• Select appropriate instrument with suitable range and precision
• Check for zero error and calibrate if necessary
• Ensure proper connection or positioning

During Measurement

• Take multiple readings to minimize random errors
• Record all readings with appropriate precision
• Note any environmental conditions affecting measurement

After Measurement

• Calculate mean values and identify outliers
• Perform error analysis
• Compare with theoretical expectations

Types of Errors

1. Systematic errors: Consistent errors from instrument faults or method
2. Random errors: Variations due to unpredictable factors
3. Zero error: Instrument reads non-zero when quantity is zero

Calculating Errors

For repeated measurements:

• Mean value: $\bar{x} = \frac{\sum x_i}{n}$
• Absolute error: $\Delta x = \frac{\text{range}}{2}$ or $\Delta x = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n(n-1)}}$
• Relative error: $\frac{\Delta x}{\bar{x}}$
• Percentage error: $\frac{\Delta x}{\bar{x}} \times 100\%$

Example 2.4: A student measures a voltage five times: 2.4 V, 2.5 V, 2.3 V, 2.5 V, 2.4 V. Calculate the mean value and error.

Solution:

Mean voltage: $\bar{V} = \frac{2.4 + 2.5 + 2.3 + 2.5 + 2.4}{5} = \frac{12.1}{5} = 2.42$ V

Range = 2.5 - 2.3 = 0.2 V

Absolute error: $\Delta V = \frac{0.2}{2} = 0.1$ V

Final measurement: $V = (2.42 \pm 0.10)$ V

Percentage error: $\frac{0.1}{2.42} \times 100\% = 4.1\%$

In Tanzania, electricians and technicians regularly use multimeters to troubleshoot electrical problems in homes and businesses. For example, when a shop owner in Mwanza reports high electricity consumption, a technician uses a multimeter to measure current draw of each appliance and a voltmeter to check voltage stability from the Tanzania Electricity Supply Company (TANESCO) supply. This systematic measurement approach helps identify faulty equipment causing excessive power use, allowing the owner to repair or replace the problematic appliance and reduce their monthly electricity bill, which can save hundreds of thousands of Tanzanian shillings each month.