Electrical and physical quantities form the foundation of instrumentation used in various professional fields across Kenya, including healthcare facilities, banks, agricultural cooperatives, and county government offices. Accurately measuring these quantities ensures proper monitoring, control, and maintenance of equipment and processes. This chapter focuses on the essential terms and practical methods for measuring electrical resistance, a fundamental property in electrical circuits and instrumentation.

4.1 Meaning of Terms

Electrical and physical measurements rely on precise terminology to describe quantities and their behavior. Understanding these terms is critical for professionals in diverse sectors such as universities, retail businesses, and hospitals to interpret instrument readings correctly.

4.1.1 Resistance

Resistance is the opposition that a material offers to the flow of electric current. It is measured in ohms (Ω) and depends on the material's nature, length, and cross-sectional area. The basic formula for resistance is:

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

where \(R\) is resistance, \(V\) is voltage across the component, and \(I\) is current through it.

Worked Examples

Example 1: A hospital equipment wire carries a current of 2 A when a voltage of 12 V is applied across it. Find the resistance.

Given: \(V = 12\,V\), \(I = 2\,A\)

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

$$ R = \frac{12}{2} $$

$$ R = 6\,\Omega $$

Answer: 6 Ω

Example 2: A sensor in a retail business system has a resistance of 10 Ω and a voltage drop of 5 V. Calculate the current flowing through it.

Given: \(R = 10\,\Omega\), \(V = 5\,V\)

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

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

$$ I = 0.5\,A $$

Answer: 0.5 A

Example 3: A cable in a county government office has a resistance of 15 Ω and carries a current of 0.8 A. Find the voltage across it.

Given: \(R = 15\,\Omega\), \(I = 0.8\,A\)

$$ V = IR $$

$$ V = 0.8 \times 15 $$

$$ V = 12\,V $$

Answer: 12 V

4.1.2 Voltage

Voltage, or electric potential difference, is the energy per unit charge provided by a source or lost across a component. It is measured in volts (V). The relationship between voltage, current, and resistance is described by Ohm’s law:

$$ V = IR $$

Worked Examples

Example 1: A farm irrigation pump motor draws 3 A through a resistance of 4 Ω. Calculate the voltage across the motor winding.

Given: \(I = 3\,A\), \(R = 4\,\Omega\)

$$ V = IR $$

$$ V = 3 \times 4 $$

$$ V = 12\,V $$

Answer: 12 V

Example 2: A temperature sensor in a hotel HVAC system has 8 Ω resistance and a voltage of 24 V across it. Calculate the current through the sensor.

Given: \(V = 24\,V\), \(R = 8\,\Omega\)

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

$$ I = \frac{24}{8} $$

$$ I = 3\,A $$

Answer: 3 A

Example 3: An industrial scale in a SACCO office has a voltage output of 9 V when a current of 0.3 A flows. Find the resistance of the scale’s load.

Given: \(V = 9\,V\), \(I = 0.3\,A\)

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

$$ R = \frac{9}{0.3} $$

$$ R = 30\,\Omega $$

Answer: 30 Ω

4.1.3 Current

Electric current is the flow of electric charge measured in amperes (A). It is the rate at which charge flows through a conductor. The current can be calculated from voltage and resistance by:

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

Worked Examples

Example 1: A laboratory instrument in a university draws 0.5 A when connected across 10 V. Calculate the resistance of the instrument.

Given: \(I = 0.5\,A\), \(V = 10\,V\)

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

$$ R = \frac{10}{0.5} $$

$$ R = 20\,\Omega $$

Answer: 20 Ω

Example 2: A water pump in an agricultural cooperative circuit has a resistance of 6 Ω and a voltage supply of 18 V. Find the current flowing.

Given: \(R = 6\,\Omega\), \(V = 18\,V\)

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

$$ I = \frac{18}{6} $$

$$ I = 3\,A $$

Answer: 3 A

Example 3: A lighting system in a county office consumes 0.75 A with a resistance of 8 Ω. Calculate the voltage across it.

Given: \(I = 0.75\,A\), \(R = 8\,\Omega\)

$$ V = IR $$

$$ V = 0.75 \times 8 $$

$$ V = 6\,V $$

Answer: 6 V

4.1.4 Ohm’s Law

Ohm’s law states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. It applies to many electrical circuits and devices used in Kenyan institutions such as banks and hospitals.

$$ V = IR $$

Worked Examples

Example 1: Calculate the current through a device with resistance 12 Ω when a voltage of 24 V is applied.

Given: \(R = 12\,\Omega\), \(V = 24\,V\)

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

$$ I = \frac{24}{12} $$

$$ I = 2\,A $$

Answer: 2 A

Example 2: A motor in a retail store has a current of 5 A and resistance of 3 Ω. Find the voltage across it.

Given: \(I = 5\,A\), \(R = 3\,\Omega\)

$$ V = IR $$

$$ V = 5 \times 3 $$

$$ V = 15\,V $$

Answer: 15 V

Example 3: A sensor in a county referral hospital has a voltage of 10 V and current 0.2 A. Calculate the resistance.

Given: \(V = 10\,V\), \(I = 0.2\,A\)

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

$$ R = \frac{10}{0.2} $$

$$ R = 50\,\Omega $$

Answer: 50 Ω

Chapter Summary

This chapter began by clarifying key terms related to electrical and physical measurements, establishing a foundation for understanding various measurement techniques. Different methods for resistance measurement were explored, including the use of voltmeter and ammeter methods, the substitution method, and the Wheatstone bridge for precise determination. Low resistance measurement techniques were then discussed, highlighting instruments such as the Kelvin bridge, four terminal resistors, low resistance linear ohmmeters, and micro-ohmmeters. The chapter proceeded to cover high resistance measurements using voltmeter and ammeter methods, the application of guard wires and guard rings to improve accuracy, Wheatstone bridge adaptations, and hand-cranked megohmmeters. Measurement of inductance and capacitance involved analyzing equivalent circuits for resistors and inductors, and introduced concepts like the Q factor of inductors and the D factor of capacitors. AC bridge theory was examined in detail, including circuit balance equations, various capacitance and inductance bridges, multifunction impedance bridges, and both analogue and digital R-C-L meters. Finally, the chapter addressed the measurement of physical quantities such as temperature, humidity, and noise, completing a comprehensive overview of electrical instrumentation techniques.