# Experiment 1 – Measurement errors and DC bridges

## Part A- Measurement errors

**Aim **To measure some unknown color coded resistors, identify & calculate measurement errors.** **

#### Apparatus

- Breadboard and wires
- 9 Volt battery or bench power supply adjusted to 9 Volt
- Colour coded resistors (6)
- Multi-meter

#### Method

- Construct the following circuit, using a nominal 9 Volt source from a battery or bench power supply. (Do not measure the voltage with a multi-meter)

For each of the colored coded resistors as “the device under test”, measure the current in each of the colored coded resistors and use Ohms law to calculate the value of the resistance under test.

(Caution: To measure current, you **must** “configure the probes to the correct inputs on the multi-meter, adjust the range switch to measure current, **then break the circuit where the current is to be measured and wire the ammeter in series. **

- Repeat the same measurement as in one, but this time measure the voltage as well as the current for each resistor. (Do not attempt to change the voltage precisely to 9 Volts between readings). Use Ohms law to calculate the resistance of each resistor under test. Make sure that you observe the caution in Method 1 to configure the multi-meter & the circuit
**between**voltage & current measurements.

- Using the resistance range on the multi-meter, measure the resistance of the color coded resistors.

- Connect all the color coded resistors in both series & parallel and measure the resistance using the multi-meter.

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#### Results

Show your results in tabular form, which enables you to compare resistances for method 1-3.

The color coded resistances were from the E24 range (see Appendix, based on your measurements 13, choose the nominal value from the E24 range of each of the color coded resistors and include it in your results.

#### Calculations

- Using the multi-meter reading as an exact value, what is the error from the nominal value in readings in method 1 & 2.
- Using the nominal E24 value of the resistors, what is the error in methods 1-3.
- Calculate and measure the resistance of the total series & parallel of the six color coded resistors

#### Discussion questions

- What are the causes of the errors in method 1, 2 and 3
- What is the error between the calculated & measured values in method 4
- What if any errors can be attributed to temperature variations during your tests

## Part B- Using DC bridge to measuring resistance

**Aim. **To measure resistance using a DC Wheatstone bridge. ** **

#### Apparatus

- Breadboard and wires
- 9Volt battery
- 2 x 10K resistors, adjustable potentiometers of varying range

(use the potentiometer that minimises the measurement error)

- Multi-meter

#### Method

- Construct the following circuit using one of the color coded resistors for the device under test. When VAB=0, the bridge is said to be balanced and
**RX=(R2.R3)/R1**

- Using a multi-meter, measure the voltage difference between the test points A & B and adjust the potentiometer R3, so that the voltage read on the meter is zero.

- Carefully disconnect one end of the potentiometer and measure the resistance value of the potentiometer which allowed the bridge to balance. Use that value to calculate the value of Rx (device under test) using the relationship

- Repeat Method 2 & 3 for all the other color coded resistors.

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**Results **

Record your measurements & results in a suitable table

**Calculations **

- Calculate the measurement error for each resistor

#### Discussion questions

- To what factors do you attribute measurement errors?
- What would be the effect if the excitation voltage for the bridge was a voltage other then 9 Volt?
- What would be the effect if the excitation voltage for the bridge was 12V AC?

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# Experiment 2 – AC bridges

## Part A- AC bridge measuring capacitance

**Aim. **To measure & confirm the value of capacitance of several capacitors wired in various combinations** **

#### Apparatus

- Breadboard and wires
- 47K resistor, 0.01uF capacitor, adjustable potentiometers of varying range

(use the potentiometer that minimises the measurement error)

- Audio signal generator, multi-meter
- 3 color coded test capacitors RED, YELLOW & GREEN

#### Method

- Construct the following circuit

- Using a multi-meter, measure the voltage difference between the test points A & B and adjust the potentiometer R3, so that the voltage read on the meter is zero. The bridge is said to be balanced.

- Carefully disconnect the “hot” end of the potentiometer and measure the resistance value which allowed the bridge to balance.

- Measure the capacitance with your multi-meter in the CAPACTANCE range

- Repeat Steps 2 , 3 & 4 for the remaining two capacitors.

- Repeat Method 2 ,3 & 4 for the following conditions.
- Any RED & GREEN capacitors in parallel
- Any GREEN & YELLOW capacitors in series
- Any YELLOW & RED parallel, combined with GREEN in series.

- Increase the frequency of the signal source to 150KHz. Attempt to re-balance the bridge using any coloured capacitor. Record your findings.

**Results **

Record your results in a suitably annotated table.

#### Calculations

- Calculate the value of each of the colored resistors using the results obtained.
- The capacitors come from the E12 range of capacitors, choose the nominal E12 value of the color coded capacitors.
- Calculate the total capacitance Method 6 (i), (ii) & (iii)

#### Discussion questions

- What are the causes errors in the bridge technique
- Derive the equation for balance for this bridge.
- In your calculations where should you “round” the values.
- What would have been the result DC excitation was used for the bridge

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## Part B- AC bridge measuring inductance.

**Aim. **To measure & confirm the capacitance of several inductors wired in various combinations using the Maxwell bridge.** **

#### Apparatus

- Breadboard and wires
- 470pF capacitor, 1K resistor, adjustable potentiometers of varying range

(use the potentiometer that minimises the measurement error)

- Audio signal generator, dual trace oscilloscope
- Three Colour coded inductors

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#### Method

- Construct the following circuit known as the Maxwell bridge.

When the Maxwell bridge is balanced by carefully adjusting

R1 & R2 the resistance and inductance can be calculated from the following equations. Rs= R2.R3/R1 & Lx = R2.R3.C1

NOTE

When Rs is very small (approx zero), then R1 will be very large approaching infinity. As the resistances of the inductors we are testing are very small, **we will not use R1 at all,** considerably simplifying the balancing operation.

- Using an oscilloscope, measure the voltage at the test points A & B
**using two CRO channels.**

- Balance the bridge by adjusting the potentiometer R2, so that the voltages at the test point are both equal in amplitude & phase.

- Switch the oscilloscope to display the difference between the two channels & note that by adjusting R2 that the difference was zero.

Re-adjust R2 as required to make the difference equal to zero again.

(You may use a “math” function in some oscilloscopes to achieve this. Please discuss with demonstrator if you have problems)

- After having balanced the bridge Carefully disconnect one end of the potentiometer and measure the resistance value which allowed the bridge to balance and use that value to calculate the value of Rx (device under test) using the relationship

- Repeat Method 3 or 4 and 5 to determine the inductance of the remaining color coded inductors.

- Decrease the frequency of the signal source to 1KHz. And attempt to rebalance the bridge. Record your findings.

- Measure the
**resistance**of inductors with a multimeter.

**Results **

Record your results in a suitably annotated table

**Calculations **

- For each inductor calculate the value of R1 which would have given a complete balance.

#### Discussion questions

- Did the fact that we did not use R1 to obtain a precise balance effect the balance that was achieved?
- Suggest and draw a simpler bridge which could be used for measuring inductance (similar to the bridge in Part A
- Give two disadvantages of such a bridge compared to the Maxwell bridge.
- What was the effect of having an excitation frequency of 1 KHz. And why? What would have been the limitation of using a multi-meter to measure the balance condition?

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# Experiment 3 – Basic transducer circuits

## Part A- Measuring temperature

**Aim. **To confirm the operation of a circuit which may be used for measuring temperature?** **

#### Apparatus

- Breadboard and wires
- 1 & 10K resistor , thermistor
- 9 Volt battery, multi-meter

#### Method

- Construct the following circuit using a thermistor and R1 = 1K

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- Measure the voltage at room temperature and with a thermometer the actual temperature.

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- Attempt to get some reading at a lower & higher temperatures by attaching the thermistor to the outside of a glass (by some method other then holding with your hands which you need to devise). Use some iced or chilled water and allow it to warm up and similarly used some hot water & allow it to cool down.
- Transpose R1 & Th in the circuit and repeat steps in 2

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**Results **

Show your results in a suitably annotated table & graph the data.

**Calculations **

- Obtain an approximate equation relating voltage to temperature

#### Discussion questions

- Does the thermistor have a positive or negative temperature coefficient
- What errors are being encountered?
- Develop & draw the circuit of a simple bridge where the voltage will be zero at room temperature (say 25 Centigrade) and will read negative for lower temperatures & positive for higher temperatures.

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## Part B- Measuring light intensity

**Aim **To confirm the operation of a circuit which may be used for measuring light intensity.

#### Apparatus

- Breadboard and wires
- 1 & 10 K resistor, LDR
- 9 Volt battery, Light source, multimeter

#### Method

- Construct the following circuit using an ORP12 Light Dependent Resistor using R1 = 10K

- Using a white light source illuminate the LDR through some transparent material which will attenuate the light. Increase the layers of the same transparent material so that almost no light illuminates the LDR.

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- Using a white light source of your choice, vary the distance between the light source source from about 0 cm to 100 cm in 10 cm. steps and record the voltages. (Attempt to reduce background light as as much as possible). Also read the voltage given by the background light.

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- Shine the light source onto a white reflective background some 10 cm. away. Also point the LDR at the same background some 30 cm away. Move the LDR toward the reflected light.

Obtain data for voltage vs distance.

- Repeat step 4 with a dark reflective background.

**Results **

Show the data in a suitably annotated table & present it graphically.

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#### Discussion questions

- Is the luminous intensity vs. thickness of attenuation layer linear or non-linear? Why?
- Is the luminous intensity vs. distance linear or non-linear. Why?
- Over what distance can the LDR function as a reflective sensor. What are the limitations?
- Develop & draw a circuit which could be used as a detector to measure the reflectivity of a material at a given distance, such that the material produces a positive voltage when it is highly reflective, a negative voltage if it is poorly reflective and 0 Volts when it is medium reflective.

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# Appendix 1: Preferred Resistor Ranges

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5 % | 1% |

10 | 10 |

11 | |

12 | 12 |

13 | |

15 | 15 |

16 | |

18 | 18 |

20 | |

22 | 22 |

24 | |

27 | 27 |

30 | |

33 | 33 |

36 | |

39 | 39 |

43 | |

47 | 47 |

51 | |

56 | 56 |

62 | |

68 | 68 |

75 | |

82 | 82 |

91 |

E12 E24

** Thermistor **

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** ****Light dependent resistor **

** ORP12 **

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# Appendix 2: Equipment Familiarization

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### 1. Multimeter

Multimeters allow measurement of voltage, current, and resistance. In recent years digital meters (commonly abbreviated to DMM for digital multimeter or DVM for digital voltmeter) have substituted the analogue meters that were used for many years in electrical works.

The multimeters we use have various input jacks that accept ‘banana’ plugs, and you can connect the meter to the circuit under test using two banana-plug leads.

Depending on how you configure the meter and its leads, it displays:

- the voltage difference between the two leads,
- the current flowing through the meter from one lead to the other, or
- the resistance connected between the leads.

Multimeters usually have a selector knob that allows you to select what is to be measured and to set the full-scale range of the display to handle inputs of various sizes. Note: to obtain the highest measurement accuracy, set the knob to the lowest setting for which the input does not cause overflow.

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### 2. Breadboard

A simple type breadboard includes sockets for plugging in components and connecting them together. Figure 1 shows a basic breadboard.

### 3. Measuring voltage and current

Voltage is always referenced to something, usually a local ground. To measure a voltage, you will first connect the ‘common’ jack of the meter to the breadboard common (i.e., breadboard ground). Next you will connect the meter’s ‘voltage’ jack to the point of interest. The meter will then tell you the voltage with respect to ground at this one point.

When connecting things, it’s always a good idea to use colour coding to help keep track of which lead is connected to what. Use a black banana plug lead to connect the ‘common’ input of the meter to the ‘ground’ jack of the breadboard. Use a red banana-plug lead with the ‘V’ input of the meter.

Example1: Measuring voltage.

Example2: Measuring current.

Note: A potentiometer is a type of resistor that has an adjustable ‘centre tap’ or ‘slider’, allowing electrical connections to be made not only at the two ends, but also at an adjustable point along the resistive material.

**4 Band Resistors Colour Code (5, 10, or 20% tolerance):**

The resistance in ohms is the sum of the values in columns 1 and 2, multiplied by the value in column 3, plus or minus the tolerance in column 4.

For example, the colour code for a 1 k resistor would be ‘brown-black-red’, for 56 Ω ‘green-blueblack’, for 330 Ω ‘orange-orange-brown’, etc.