Part 103-108: Resistors and Resistance Assignment 1 - Answers with Commentary

Question 1

How does an increase in length affect a conductors resistance?

Assuming a constant cross-sectional area, an increase in length will increase a conductor's resistance.

Question 2

What are 4 other factors that affect resistance?

This question is somewhat broad and open-ended.

The resistance of a conductor is given by \( R = \frac{\rho L}{A} \), where \( R \) is the resistance (Ω), \( \rho \) is the resistivity (Ωm), \( L \) is the length (m), and \( A \) is the conductor cross-sectional area (m²). The length \( L \) is already accounted for in Question 1.

The resistance equation gives us two more factors:

• Resistivity.
• Conductor area.

Resistivity is affected by conductor material, and temperature.

Further, some resistors are affected by other environmental conditions like light levels (light dependent resistors), applied voltage (voltage dependent resistors) and such.

So a set of four factors could be anything from the list below.

• Resistivity.
• Conductor area.
• Conductor material.
• Temperature.
• Light level.
• Voltage.

The question is so broad that there will doubtless be others.

Question 3

Write the unit symbol for the measurement of resistance.

The symbol is 'Ω'.

The symbol is the Greek capital letter omega.

Question 4

Write the formula for resistivity.

The resistance formula as a function of resistivity is \( R = \frac{\rho L}{A} \).

Rearranging this gives \( \rho = \frac{RA}{L} \).

Note there may be other formulas for resistivity depending on circuit and experimental conditions. This question is quite broad.

Question 5

Write the unit of measurement for resistivity.

The unit of measurement is ohm-metre, or Ωm.

Other forms are used, such as µΩm, but the basic unit is the one without a prefix.

It is not clear from the question which form is desired.

NOTE: The unit of measurement for resistivity is not \( \rho \). That is the symbol for resistivity in equations.

Question 6

What does tempco stand for?

In its broadest interpretation, the term "tempco" is short for "temperature coefficient".

It is not clear from the question whether it is looking for the answer "temperature coefficient", or a more specific term like "temperature coefficient of resistance".

Question 7

What does \( R_0 \) stand for?

It is assumed this question is talking about calculating resistance as a function of temperature.

The term \( R_0 \) stands for the resistance of a sample at 0°C.

Question 8

What is the resistivity of copper?

This question is quite broad, as there are many different forms of copper conductor (annealed, hard drawn, oxygen-free copper, tough pitch) in use. Further, the resistivity of copper varies with temperature.

A reasonable answer is something like 1.68 × 10⁻⁸ Ωm at 20°C.

Question 9

Explain the difference between a linear and non-linear resistor.

This question can have a couple of differeent interpretations.

• In circuit analysis, a linear resistor is a resistor with a resistance independent of the voltages and currents in a circuit.
• Another interpretation is a resistor whose value does not change in response to external circuit conditions.

An example of the difference is a thermistor: a thermistor's resistance changes with temperature. But if it is used within ratings, the relationship between voltage and current will be linear.

Question 10

What is the difference between a fixed and variable resistor?

This question is quite broad, because the term "variable resistor" could encompass any device that has a resistance that is not constant. The answer assumes that the answer is based on the behaviour of decives like potentiometers or rheostats.

This question can have a couple of differeent interpretations.

• A resistor that is designed and manufactured to have a resistance that can be changed. This covers devices like rheostats, potentiometers and such.
• A device that has a variable resistance by any means (except perhaps overloading and destruction). This would cover the devices above, as well as thermistors, light dependent resistors etc.

Question 11

Give an example of each of the 2 terms for Q9 and 2 terms for Q10.

All of the factors affecting the scope of Questions 9 and 10 will be kept in mind.

Some answers are as follows.

• Linear Resistor: These are ordinary "resistors".
• Non-linear Resistor: Something like a voltage-dependent resistor. The behaviour is non-linear, but is designed to be predictable and repeatable.
• Fixed Resistor: These are ordinary "resistors".
• Variable Resistor: Potentiometers, rheostats and such. I would also argue that thermistors and light-dependent resistors would also fall under this category, as their resistance only depends on external conditions, and not voltages and currents.

Question 12

What metal is used in a wire wound resistive element?

This question is quite broad, because the conductor used in a resistive element is application driven.

Some important factors to consider when choosing resistance wire are as follows.

• The design temperature of the element.
• The design heat output the element.
• Whether the element is clad or exposed directly to the substance it is heating.
• Chemical reactivity.
• How stable the resistance is with temperature. Having a similar cold resistance is desirable to reduce in-rush current.
• Weight.
• Physical durability.

That said, copper is rarely used as a resistive element, because it is too good a conductor. Copper heating elements would be impractically thin and delicate.

The most common choice for heating elements is nichrome. Nichrome is an alloy of Nickel and Chromium, and is designed to optimise all the requirements for a good heater element.

Question 13

Explain why a VDR is wired in parallel with the load?

The term VDR stands for "voltage dependent resistor". These may also be referred to as a metal-oxide varistor, MOV, varistor, transient suppressor, or any other suitable name.

The resistance of a MOV only depends on the applied voltage. The resistance varies with the voltage, so that a MOV will "clamp" the voltage at a certain maximum level by diverting current through itself. This current is independent of the load current.

In other words, in order to control the voltage across the load, the MOV must go in parallel with the load.

Question 14

Why does an LDR use a bi metal switch to operate a luminare?

This question assumes that the LDR is in a bi-metal switch circuit. Modern controllers may use an LDR with electronics and relays to achieve the same objective. Further, many streetlights in New Zealand do not have a light sensor ar all. They are controlled from a central "ripple-control" system that turns on all streetlights on or off at once.

An LDR driven bi-metal switching system uses an LDR to control the amount of current flow through a resistive heater attached to a bi-metal strip.

The bi-metal strip is configured so that if it is heated, it will bend and open a set of switch contacts.

If the bi-metal strip becomes cold enough, it will relax and close the set of switch contacts.

The LDR controls the amount of current flowing through the strip heater.

When it is light, the LDR has a low resistance, which allows enough current to flow to heat the bi-metal strip. The bi-metal strip bends and opens the contacts, turning off and keeping the light off.

When it is dark, the LDR has a high resistance, which reduces the current to flow available to heat the bi-metal strip. The bi-metal strip relaxes and closes the contacts, turning on and keeping the light on.

Question 15

What application is common for a wire wound resistor?

Wire wound resistors are commonly used for high power dissipation (5 W and up) and high temperature resistors.

Wire wound resistors are commonly used as temperature sensors e.g. PT100 temperature sensors which are a wire wound platinum coil resistor for sensing temperature.

Question 16

What application is common for a PTC thermistor?

Here are a couple of applications for PTC thermistors:

• Self-regulating heaters. A chip of PTC material acts as a low resistance until its temperature reaches a certain level, where it will "flip" to a high resistance state. The thermistor will then "ride the line", at the temperature where the self-heating from the resistance matches the heat loss.
  
  The temperature where this happens depends on the PTC material. This arrangement allows for very simple temperature control without requiring any thermostats or control circuits.
  
  
• Overcurrent protection. If the current flow through a PTC thermistor gets too high, the thermistor will heat and "flip" to a high resistance state. It will stay this way as long as it remains at a high temperature. The PTC can be reset by allowing it to cool.
  
  
• Motor Starting. Refrigerator motors are sealed inside a gas-tight enclosure. Any starting mechanism that relies on moving parts in the motor (e.g. centrifugal switch) is undesirable due to the inaccessibility for maintenance, and contamination from sparking. An alternative method of starting the motor consists of a PTC thermistor connected to the start winding. The PTC thermistor allows the start winding to get the motor running, then after a time "flips" to a high resistance state, keeping the start winding from burning out.

Question 17

Name each of the 7 resistors on the front of this workbook

See the marked-up picture below. The relevant resistors are numbered 1 through 7.

The types of resistors are given in the table below.