Electrical quantities form the fundamental basis of many measurements and experiments in a science laboratory setting. Understanding how to measure voltage, current, and resistance accurately is essential for laboratory technologists working with electrical circuits, instrumentation, and equipment calibration. In Kenya, laboratory professionals often engage with devices that require precise electrical measurements to ensure safety, reliability, and compliance with standards.

2.1 Electrical quantities

Electrical quantities describe the core parameters of electrical circuits and devices. In laboratory technology, accurate measurement of these quantities supports experimental integrity and equipment functionality. The main electrical quantities are voltage (volt), current (ampere), and resistance (ohm), each with specific units and measurement techniques.

2.1.1 Volt

Voltage, measured in volts (V), represents the electric potential difference between two points in a circuit. It indicates the energy per unit charge available to drive current through a conductor.

The governing formula for voltage is given by Ohm’s Law:

$$ V = IR $$

where \( V \) is voltage in volts, \( I \) is current in amperes, and \( R \) is resistance in ohms.

Worked Examples

Example 1: A laboratory circuit has a resistance of 10 ohms and a current of 2 amperes flowing through it. Calculate the voltage across the resistor.

Given: \( R = 10 \, \Omega \), \( I = 2 \, A \)

$$ V = IR $$

$$ V = 2 \times 10 $$

$$ V = 20 \, V $$

Answer: 20 volts

Example 2: In an experiment, a voltage of 12 V is applied across a resistor of 4 ohms. Calculate the current flowing through the resistor.

Given: \( V = 12 \, V \), \( R = 4 \, \Omega \)

Rearranged formula:

$$ I = \frac{V}{R} $$

$$ I = \frac{12}{4} $$

$$ I = 3 \, A $$

Answer: 3 amperes

Example 3: A voltage source delivers 24 V across a circuit with a current of 0.5 A. Find the resistance of the circuit.

Given: \( V = 24 \, V \), \( I = 0.5 \, A \)

Rearranged formula:

$$ R = \frac{V}{I} $$

$$ R = \frac{24}{0.5} $$

$$ R = 48 \, \Omega $$

Answer: 48 ohms

Example 4: In a laboratory setup, a current of 0.25 A flows through a resistor of 100 ohms. Determine the voltage across the resistor.

Given: \( I = 0.25 \, A \), \( R = 100 \, \Omega \)

$$ V = IR $$

$$ V = 0.25 \times 100 $$

$$ V = 25 \, V $$

Answer: 25 volts

Example 5: A voltage of 48 V is applied to a circuit with a resistance of 12 ohms. Calculate the power dissipated in the resistor using the voltage value.

Given: \( V = 48 \, V \), \( R = 12 \, \Omega \)

Power formula:

$$ P = \frac{V^2}{R} $$

$$ P = \frac{48^2}{12} $$

$$ P = \frac{2304}{12} $$

$$ P = 192 \, W $$

Answer: 192 watts

2.1.2 Current

Electric current, measured in amperes (A), is the rate of flow of electric charge through a conductor. Current measurement is critical in laboratory experiments involving electrical circuits and devices.

The fundamental formula for current is:

$$ I = \frac{Q}{t} $$

where \( I \) is current in amperes, \( Q \) is electric charge in coulombs, and \( t \) is time in seconds.

Worked Examples

Example 1: A charge of 10 coulombs passes through a wire in 5 seconds. Calculate the current.

Given: \( Q = 10 \, C \), \( t = 5 \, s \)

$$ I = \frac{Q}{t} $$

$$ I = \frac{10}{5} $$

$$ I = 2 \, A $$

Answer: 2 amperes

Example 2: During an experiment, a current of 3 A flows for 20 seconds. Find the total charge transferred.

Given: \( I = 3 \, A \), \( t = 20 \, s \)

Rearranged formula:

$$ Q = It $$

$$ Q = 3 \times 20 $$

$$ Q = 60 \, C $$

Answer: 60 coulombs

Example 3: A current of 0.5 A is maintained in a circuit for 2 minutes. Calculate the total charge moved.

Given: \( I = 0.5 \, A \), \( t = 2 \, \text{minutes} = 120 \, s \)

$$ Q = It $$

$$ Q = 0.5 \times 120 $$

$$ Q = 60 \, C $$

Answer: 60 coulombs

Example 4: An electrical device draws a current of 4 A for 30 seconds. Calculate the total charge delivered.

Given: \( I = 4 \, A \), \( t = 30 \, s \)

$$ Q = It $$

$$ Q = 4 \times 30 $$

$$ Q = 120 \, C $$

Answer: 120 coulombs

Example 5: A charge of 100 coulombs flows through a conductor in 25 seconds. Determine the current.

Given: \( Q = 100 \, C \), \( t = 25 \, s \)

$$ I = \frac{Q}{t} $$

$$ I = \frac{100}{25} $$

$$ I = 4 \, A $$

Answer: 4 amperes

2.1.3 Ohm

Resistance, measured in ohms (Ω), quantifies how much a material opposes the flow of electric current. The unit ohm is named after Georg Simon Ohm, and resistance is a key parameter in circuit analysis and laboratory measurements.

Ohm’s Law relates resistance to voltage and current:

$$ R = \frac{V}{I} $$

where \( R \) is resistance in ohms, \( V \) is voltage in volts, and \( I \) is current in amperes.

Worked Examples

Example 1: A voltage of 9 V causes a current of 3 A to flow through a resistor. Calculate its resistance.

Given: \( V = 9 \, V \), \( I = 3 \, A \)

$$ R = \frac{V}{I} $$

$$ R = \frac{9}{3} $$

$$ R = 3 \, \Omega $$

Answer: 3 ohms

Example 2: In a laboratory circuit, the resistance is 15 ohms and the current is 0.4 A. Find the voltage across the resistor.

Given: \( R = 15 \, \Omega \), \( I = 0.4 \, A \)

$$ V = IR $$

$$ V = 0.4 \times 15 $$

$$ V = 6 \, V $$

Answer: 6 volts

Example 3: A resistor has a voltage drop of 24 V and a current of 0.8 A. Determine its resistance.

Given: \( V = 24 \, V \), \( I = 0.8 \, A \)

$$ R = \frac{V}{I} $$

$$ R = \frac{24}{0.8} $$

$$ R = 30 \, \Omega $$

Answer: 30 ohms

Example 4: A circuit has a voltage of 120 V and a resistance of 40 ohms. Calculate the current flowing.

Given: \( V = 120 \, V \), \( R = 40 \, \Omega \)

$$ I = \frac{V}{R} $$

$$ I = \frac{120}{40} $$

$$ I = 3 \, A $$

Answer: 3 amperes

Example 5: In an experiment, a current of 5 A flows through a resistor causing a voltage drop of 60 V. Find the resistance and verify power dissipated.

Given: \( I = 5 \, A \), \( V = 60 \, V \)

$$ R = \frac{V}{I} $$

$$ R = \frac{60}{5} $$

$$ R = 12 \, \Omega $$

Power dissipated:

$$ P = VI $$

$$ P = 60 \times 5 $$

$$ P = 300 \, W $$

Answer: Resistance = 12 ohms, Power = 300 watts

Chapter Summary

This chapter introduced the fundamental electrical quantities including volt, current, and ohm, establishing the basis for understanding electrical measurements. It then explored electrical circuits, highlighting how these quantities interact within different components. Various electrical measuring instruments were examined, such as the voltmeter, ammeter, ohmmeter, and multimeter, detailing their functions and applications. The chapter also discussed factors affecting resistance, emphasizing temperature, material, and dimensions as key influences. Resistor networks were analyzed to demonstrate how resistors combine in series and parallel arrangements. Techniques for converting a moving coil galvanometer into an ammeter or voltmeter were explained to enhance measurement versatility. Further, the concepts of capacitance and inductance were introduced as essential electrical properties in circuits. Finally, the importance of accurate report writing on electrical quantity measurement practicals was underscored to ensure proper documentation and analysis of experimental results.