Part 103-108: Resistors and Resistance Worksheet 18A - Answers with Commentary
Introduction
Conductor resistance is an important part of any electrical installation - excessive conductor resistance increases power losses and voltage drop. Apart from being wasteful of energy, excessive heating can cause deterioration of the insulation around wires.
Insulation is the other essential component of an installation. Insulation protects against short circuit, leakage current, and electric shock. All installations must be tested to make sure that the separation between live parts and earth is sufficient to protect from short circuit, leakage current, and electric shock.
Insulation acts as a large number of resistances in parallel with the power supply. The path these currents take is sometimes referred to as leakage. This also means that the more length of insulation there is, the lower the insulation resistance,
since there are more leakage paths in a longer cable.
Insulation Resistance Testing
NOTE: The information in this section is a simplified summary. The full requirements for insulation resistance testing are laid out in § 8.3.6 of AS/ANZ3000:2007 (The Wiring Rules). The Wiring Rules should always be consulted in the first instance.
Insulation resistance testing is carried out at a high voltage. The normal voltage for testing insulation resistance in a single phase installation is 500 V dc. The figure of 500 V is used because the peak value of the 230 V ac waveform is abour 325 V. A 500 V potential stresses the insulation beyond it's rating, so that if it passes at 500 V, it will also be ok with 230 V ac.
The device that carries out insulation testing is called an insulation resistance tester. An insulation resistance tester may also be referred to as a Megger, but Megger is a trademark name. That said, "to Megger an installation" will be universally understood as performing insulation testing.
The requirements for insulation resistance testing are laid out in § 8.3.6 of AS/ANZ3000:2007 (The Wiring Rules).
A table showing simplified insulation resistance requirements is below. All insulation resistance tests are between live parts (live and/or neutral) and earth. Unless you know specifically otherwise, always use a minimum insulation resistance value of 1 MΩ. Most of the time, insulation resistance values are given and processed in megohm (MΩ) values.
| Minimum Value |
Applicable Situations |
|---|---|
| 1 MΩ |
All situations, except where noted below. |
| 0.01 MΩ |
Sheathed heating elements of appliances (e.g. stove elements or hot water elements). |
| 0.05 MΩ |
Appliances or fittings with a functional earth. The functional earth is a connection to earth that is required for the appliance or fitting to function, but is not used to carry an overload current, leakage current, or short circuit current. |
A table showing simplified insulation resistance testing voltage requirements is below. All insulation resistance tests are between live parts (live and/or neutral) and earth. Unless you know specifically otherwise, always use a test voltage of 500 V.
| Testing Voltage |
Applicable Situations |
|---|---|
| 500 V |
All situations, except where noted below. |
| 250 V |
Some devices may contain surge protective devices, that will prevent the test voltage being able to get to 500 V, or will otherwise be damaged. If this is the case, the test voltage may be reduced to 250 V dc. |
Insulation Resistance of Cables
The insulation resistance of a cable is proportional to how much current can leak through the cable insulation. The shorter the cable, the fewer paths there are.
- The shorter the cable, the higher the insulation resistance.
- The longer the cable, the lower the insulation resistance.
The insulation resistance is also affected by the following features of the cable itself.
- Cable length (already discussed above).
- Insulation material. Different insulation materials have different resistivity.
- Insulation condition. Insulation that is in good condition has higher insulation resistance.
- Insulation age. Older insulation tends to have lower insulation resistance.
- Insulation thickness. Thicker insulation has higher resistance.
- Moisture. Moisture in or around cables and terminations can decrease insulation resistance.
- Contamination. Contamination (e.g. salt, animal residues) in or around cables and terminations can decrease insulation resistance.
- Physical damage. Physical damage (e.g. physical impact, animal activity) in or around cables and terminations can decrease insulation resistance.
- Electrical damage. Electrical damage (e.g. overload, overheating, overvoltage) can cause damage to the insulation that can decrease insulation resistance.
All cables have a "cable constant" \( \rho \), that governs how the insulation resistance varies with length. \( \rho \) has the unit Ωm (or any suitable prefix), and is equal to the product of the insulation resistance and the length of the cable. The value is equivalent to resistivity.
The basic equation for \( \rho \) is given below.
\(\rho = R_1 L_1 \)
where \( \rho \) is the cable constant, \( R_1 \) is the insulation resistance of the cable sample, and \( L_1 \) is the length of the cable sample.
When \( \rho \) is known, the insulation resistance, or length of cable can be calculated for a different sample of cable.
- \( R_2 = \frac{\rho}{L_2} \), where \( R_2 \) is the insulation resistance of the different cable sample, and \( L_2 \) is the length of the different cable sample.
- \( L_2 = \frac{\rho}{R_2} \), where \( R_2 \) is the insulation resistance of the different cable sample, and \( L_2 \) is the length of the different cable sample.
Question 1
Fill in the blanks...
Insulation Resistance (abbreviated to IR in the rest of this "work sheet") can be considered as a number of resistors connected in parallel, consequently, as the length of a cable is increased the IR will decrease, and conversely as the length of a cable decreases the IR will increase.
As noted above, the insulation resistance is equal to a constant (\(\rho\)) divided by the length. Or, insulation resistance is inversely proportional to length. An inverse relationship means that if one variable goes up, the other must come down, and vice versa.
Question 2
List 5 factors that will affect the IR of a cable.
Any of the five factors above will be acceptable.
Question 3
Fill in the blanks...
IR is measured with an insulation resistance tester (the term MEGGER is a trade name and should not be used in exam answers). This type of device tests IR with an average voltage of 500 Volts d.c., which is designed to stress the insulation above that normally applied by the mains voltage to see if the insulation will breakdown with the additional stress. The normal unit for values of IR is the MΩ.
Question 4
A cable which is 50 m long has an IR test result of 10 MΩ. What is the IR of 200 m of the same cable?
Solution
We have a sample length (50 m), and a sample resistance (10 MΩ).
We can calculate \( \rho \).
\( \rho = R_1 L_1 = 50 \cdot 10 = \) 500 MΩm.
NOTE: We do not have to convert the unit of \( \rho \) to Ωm, as long as we stay mindful of how units are handled in our calculations.
The insulation resistance of the 200 m length of cable can be calculated using \( \rho \).
\( R_2 = \frac{\rho}{L_2} = \frac{500}{200} = \) 2.5 MΩ #.
Question 6
A 100 m long drum of cable has an IR of 100 MΩ. What is the IR of 75 m?
Solution
We have a sample length (100 m), and a sample resistance (400 MΩ).
We can calculate \( \rho \).
\( \rho = R_1 L_1 = 400 \cdot 100 = \) 40000 MΩm.
The insulation resistance of the 75 m length of cable can be calculated using \( \rho \).
\( R_2 = \frac{\rho}{L_2} = \frac{40000}{75} = \) 533.3 MΩ (4 sf) #.