Electrical instrumentation professionals in Kenya must accurately measure electrical quantities to ensure equipment functionality and safety across many sectors such as healthcare, education, finance, and agriculture. Resistance measurement is fundamental for diagnosing circuit conditions, verifying component specifications, and preventing faults. This chapter covers methods for measuring resistance, interpreting resistor color codes, and techniques for measuring high resistance values using specialized instruments.

3.1 Resistance measurement

Resistance measurement is essential in maintaining electrical devices and systems in diverse Kenyan workplaces, from county government offices to retail businesses. Accurate resistance values help detect faults like short circuits and open circuits, ensuring proper operation and safety. Various methods exist to measure resistance directly and indirectly, depending on the application and required precision.

3.1.1 Methods of resistance measurement

Resistance measurement can be performed using several techniques, each suitable for different accuracy levels and resistance ranges. The most common methods include using an ohmmeter, the Wheatstone bridge, and the volt-ampere method.

The fundamental formula governing resistance measurement is Ohm's law:

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

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

Worked Examples

Example 1: A technician at a county referral hospital needs to measure the resistance of a sensor wire. The measured voltage across the wire is 2 V, and the current flowing is 0.5 A. Find the resistance.

Given: \(V = 2\,V\), \(I = 0.5\,A\)

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

$$R = \frac{2}{0.5}$$

$$R = 4\,\Omega$$

Answer: 4 \(\Omega\)

Example 2: In a university laboratory, a student applies a voltage of 12 V across a resistor and measures a current of 0.2 A. Calculate the resistance.

Given: \(V = 12\,V\), \(I = 0.2\,A\)

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

$$R = \frac{12}{0.2}$$

$$R = 60\,\Omega$$

Answer: 60 \(\Omega\)

Example 3: A SACCO office technician uses a Wheatstone bridge to measure an unknown resistance. The bridge is balanced when the ratio of resistances is such that \(R_1 = 100\,\Omega\), \(R_2 = 200\,\Omega\), and \(R_3 = 150\,\Omega\). Find the unknown resistance \(R_x\).

Given: \(R_1 = 100\,\Omega\), \(R_2 = 200\,\Omega\), \(R_3 = 150\,\Omega\)

The Wheatstone bridge balance condition is:

$$\frac{R_1}{R_2} = \frac{R_x}{R_3}$$

Rearranged to find \(R_x\):

$$R_x = \frac{R_1}{R_2} \times R_3$$

$$R_x = \frac{100}{200} \times 150$$

$$R_x = 0.5 \times 150$$

$$R_x = 75\,\Omega$$

Answer: 75 \(\Omega\)

Example 4: At a retail business, a volt-ampere method is used to measure resistance. The voltmeter reads 5 V, and the ammeter reads 0.1 A. Calculate the resistance.

Given: \(V = 5\,V\), \(I = 0.1\,A\)

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

$$R = \frac{5}{0.1}$$

$$R = 50\,\Omega$$

Answer: 50 \(\Omega\)

Example 5: In an agricultural cooperative, a technician measures a resistance using the volt-ampere method. The voltage is 24 V, and the current is 0.3 A. Find the resistance.

Given: \(V = 24\,V\), \(I = 0.3\,A\)

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

$$R = \frac{24}{0.3}$$

$$R = 80\,\Omega$$

Answer: 80 \(\Omega\)

3.1.2 Resistor color coding

Resistor color coding is a universal system used to identify resistor values and tolerances. Understanding this code is crucial for professionals in various sectors, such as county government offices, to quickly determine component specifications without measuring devices.

Resistor color codes represent numerical values and tolerance using colored bands painted on the resistor body. The standard code consists of four or five bands, each indicating a digit, multiplier, or tolerance.

The formula to calculate resistance from color bands is:

$$R = (AB) \times 10^C$$

where \(A\) and \(B\) are the first two digits, and \(C\) is the multiplier.

Worked Examples

Example 1: A resistor has color bands Brown, Black, Red, Gold. Find its resistance and tolerance.

Color codes:

• Brown = 1

• Black = 0

• Red = multiplier \(10^2\)

• Gold = ±5% tolerance

Calculate resistance:

$$R = (10) \times 10^2$$

$$R = 10 \times 100$$

$$R = 1000\,\Omega$$

Answer: 1000 \(\Omega\) ±5%

Example 2: A resistor has color bands Red, Violet, Orange, Silver. Calculate its resistance and tolerance.

Color codes:

• Red = 2

• Violet = 7

• Orange = multiplier \(10^3\)

• Silver = ±10% tolerance

Calculate resistance:

$$R = (27) \times 10^3$$

$$R = 27 \times 1000$$

$$R = 27000\,\Omega$$

Answer: 27000 \(\Omega\) ±10%

Example 3: In a hotel maintenance workshop, a resistor has bands Yellow, Violet, Brown, Gold. Find the resistance and tolerance.

Color codes:

• Yellow = 4

• Violet = 7

• Brown = multiplier \(10^1\)

• Gold = ±5% tolerance

Calculate resistance:

$$R = (47) \times 10^1$$

$$R = 47 \times 10$$

$$R = 470\,\Omega$$

Answer: 470 \(\Omega\) ±5%

Example 4: A resistor in a retail business circuit has color bands Orange, Orange, Black, Brown. Determine its resistance and tolerance.

Color codes:

• Orange = 3

• Orange = 3

• Black = multiplier \(10^0\)

• Brown = ±1% tolerance

Calculate resistance:

$$R = (33) \times 10^0$$

$$R = 33 \times 1$$

$$R = 33\,\Omega$$

Answer: 33 \(\Omega\) ±1%

Example 5: A resistor in a university lab has bands Green, Blue, Yellow, Gold. Find the resistance and tolerance.

Color codes:

• Green = 5

• Blue = 6

• Yellow = multiplier \(10^4\)

• Gold = ±5% tolerance

Calculate resistance:

$$R = (56) \times 10^4$$

$$R = 56 \times 10000$$

$$R = 560000\,\Omega$$

Answer: 560000 \(\Omega\) ±5%

Chapter Summary

This chapter covered essential techniques for measuring electrical quantities, beginning with resistance measurement methods including the use of various instruments and the interpretation of resistor color codes for identifying resistance values. It then explored high resistance measurement with a focus on the hand-cranked megohmmeter, a key tool for testing insulation and detecting faults. Voltage measurement techniques were discussed next, emphasizing accuracy and proper instrument usage. Current measurement methods followed, highlighting different devices suitable for various current ranges. The chapter also addressed insulation resistance measurement, critical for ensuring electrical safety and system reliability. Finally, the chapter outlined important OSHA regulations that govern safe practices when working with electrical instrumentation, underscoring the importance of compliance to prevent accidents and injuries.