# Linear And Non Linear Voltage Divider Engineering Essay

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Published: *Mon, 5 Dec 2016*

The report describes an investigation of how linear and non-linear voltage divider type of circuit relies on the application of Ohm’s law (1).

The linear circuit was consisted of series resistors. Separating the total resistance of the circuit into two parts, the circuit functions as a voltage divider across which output voltages, and are taken. The report hence is also study the operation of a voltage divider and finds that the total voltage drop around a single close path divides among the series resistors in amounts directly proportional to the resistance values (2) so the formula where and are the output voltages across the resistance and respectively was derive.

The investigation was conduct under range of DC and AC input voltages so the ratio between the output voltages was compared to the required ratio of 2:1. This was successfully matched within the tolerance of ±5% thus; the proportionality of the output voltages to the input voltages proves the linearity of the circuit and it applicability to Ohm’s law.

The non-linear circuit was consisted of 1kâ„¦ resistor and a filament bulb. The investigation was conduct under range of DC and AC input voltages and shows that the recorded measurement of the output voltage across the bulb, , was not showing linear trend with respect to the input voltage, . Inspection of the IV chrematistic of the filament bulb shows that the bulb is a non-ohmic conductor. Looking at the linear band the resistance of 61.2 â„¦ was found

## Introduction

## Work objective

Choosing the right apparatus and components is essential when designing electronic circuits. This needs to be done carefully so the measurements will be as accurate as possible. This report aims to find a procedure of choosing the right resistors and the method of using them. This concept together with how to recognise resistors values, measuring potential difference across a component and the physics of the filament bulb will be examined in the background to the experiment work.

Understanding the specification set out in the task is key factor in completing the practical work. The report will examine the theory applied to the voltage divider and by using the definition of current, voltage, electrical resistance and power, the report will obtain the voltage divider formula and the assumption that these formula are based on. The report will then present the prediction based on the theory.

The report will show the method of how the wide range of reading is to be taken and explain which variables are going to change and which variables will be kept the same. Also, the particular method to test the prediction and completing the exercise script will be presented as well as the reason for why this method was chosen.

Finally, the report will analyze one of the simple basic circuits: the voltage divider. The report will evaluate the evidence and procedures and a comment on the accuracy and reliability of the result. The last section will suggest ways the measurement could be made more accurate and reliable and how this experiment might be extended.

## Background to the experimental work

## RESISTOR POWER RATINGS

The amount of power in a resistor is important because the power rating of the resistor must be high enough to handle the expected power in the circuit. The resistors used in this experiment are type CRF16. These have small case size and full power rating of 0.25 W. To specify the required minimum resistance the following procedure is adopted:

Determine the total resistance: The total series resistance, , is the sum of all resistors in the series circuit.

Next, the current, , need to be calculated. When resistors are connected in series and a voltage is applied across the series connection, there is only one path for current; therefore each resistor in series has the same amount of current through it. Using Ohm’s law which states that the current is directly proportional to voltage and inversely proportional to resistance (1) the equation:

where, is the source voltage is derive. Then the power, , in each resistor is:

Substituting (1.1-2) into (1.1-3), the following equation is obtained:

rearranging to rescue :

## THE RESISTORS COLOR CODES

The resistors used in this experiment are common fix resistor constructed using carbon film. The resistive carbon evenly distributed along the high-grade ceramic rod. In order to differentiate between the resistors value and confirming the values and tolerance when they are connected to the circuit, a color coding system is used. The resistors used in this experiment are coded with four bands. The first and the second band closer to the end represent the first and second digit respectively. The third band represents the multiplier, i.e. the number of zeros following the second digit. In this experiment the last band represent tolerance value of ±5% and it is a gold color. The table in appendix 3 shows the resistance value of a resistor with 4-band color code.

## MEASURING VOLTAGE

A DMM has a “floating” common, so it can be connected to any point in the circuit and read the correct voltage between the two leads.

Measuring voltage with oscilloscope may create a grounding problem since the generator and the oscilloscope have a common ground. The problem occurs when trying to measure the voltage across the component that is not connected to ground. Trying to do so, will effectively short out of the circuit all the components that connected from the terminal at which the measurement is taken to the ground terminal and the voltage measured is meaningless. This is become very important when current sensitive components like the filament bulb are connected in the circuit. The resistor is therefore the current limiting impedance. Shorting out the resistor could raise the current to levels that could cause permanent damage to the bulb. The solution to the problem is usually to recognise the grounding points of the circuit and connecting the oscilloscope to these points only. To find out the voltage across the component which is not connected to ground, the method used is to subtract the measured voltage from the input voltage

## THE FILAMENT LAMP (7)

The filament is made of tungsten wire and it is essentially a device for converting electrical input energy into an output of radiant energy in the form of light and heat. According the temperature at which the filament glows will determine the appearance of the light emitted. The tungsten wire is very fine in diameter; the wire is coil as shown in Fig. 1.1.4-1.

The closer the spacing of the coils the hotter the filament can operate.

The filament lamp to be used in this experiment is yellow filament lamp size 4mm and it is rated at 12V, 30mA with output energy of 0.7 Lumens. The ideal operation condition for AC is stabilized 50Hz. This bulb is sensitive to operation with DC as the one direction current flow causes an effect named ‘DC notching’ where the filament wire is becoming weak. The report will define the metal (tungsten) filament lamp device by the current voltage (I/V) characteristics and will explain the difference in behavior of the tungsten filament light bulb.

## Figure .1.4-1 Single Coil filament (7)

## UNCERTAINTY IN CALCULATED VALUES (8)

The arithmetic mean ratio, , will be calculated by the following equation:

(1.1.5-1)

where can have any integer value, is the number of observations and represent any of the observation. Having obtained a mean value, , the precision of the experiment will be quantified by using the equation for standard deviation, , for the special case where all data points have equal weight

(1.1.5-2 )

The standard deviation, defined by Eq. (1.1.5-2) provides the random uncertainty estimate for any one of the measurements used to compute . The standard deviation of the mean value of a set of measurements , when all measurement have equal statistical weight is given by

The results in this report will be stated in term of the percent or fractional uncertainty, . Multiply by 100. The relationship between and is as follows

## Theory

## Governing equations

This section will consider a single-loop circuit, as shown in figure 2.1-1 in order to develop the equations relative to the experiment. The direction of the resistor voltages and current are marked according the convention set by Ohm’s law:

Electron flow current is defined to be into the negative side of each resistor and out of the negative side of each resistor and out of the more positive (less negative) side. With regards to the source – electrons flow current is defined to be out of the negative side of a source and into the positive side.

## Figure .1-1 Single-loop circuit with voltage source vs.

Using Kirchhoff’s current low at each node. The following four equations can be obtained:

(2.1-1) a:

(2.1-2) b:

(2.1-3) c:

(2.1-4) d:

Each of these equations can be derived from the other three equations. Since the current is the same at all point in a series circuit the following equation is noted:

so that the current can be said to be the loop current and flows continuously around the loop from a to b to c to d and back to a. The connection of resistor is Fig 2.1-1 is said to be a series connection since all the elements carry the same current. In order to determine, we use the principle of superposition where voltage sources in series add algebraically and Kirchhoff’s voltage low around the loop: The sum of all voltage drops around a single closed path in a circuit is equal to the total source voltage, in that loop.

(2.1-5)

where are the voltage across the resistors . Also from Kirchhoff’s voltage law: The algebraic sum of all the voltages (both source and drops) around a single closed path is zero. The voltage drops in a circuit are always opposite in polarity to the total source voltage. Eq. (2.1-5) can be written as:

(2.1-6)

Using Ohm’s law for each resistor, Eq. (2.1-6) can be written as:

Solving for , we have

Thus, the voltage across the nth resistor is and can be obtained as

A voltage drop results from a decrease in energy level across the resistor.

A voltage divider is a series arrangement of resistor connected to a voltage source. Thus, the voltage appearing across one of a series resistors connected in series with a voltage source will be the ratio of its resistance to the total resistance.

This circuit shown in Fig 2.1-2 demonstrates the principle of voltage division, and the circuit is called a voltage divider or potential divider

In general, the voltage divider principle is represented by the equation

where , is the voltage across the nth resistor of N resistors connected in series.

A voltage divider is so named because the voltage drop across any resistor in the series circuit is divided down from the total voltage by an amount proportional to that resistance value in relation to the total resistance.

Comparing the circuit shown in figure 2.1-1 and the circuit shown in figure 2.1-2, the current are identical when and the resistance is said to be an equaivient resistance of the series connection of resistors and .

To determine the resistance and required so that the ratio between the voltages cross and will be 2:1 we consider the voltage across the first resistance

And across the second resistance

The lab script desire, so division of the first equation in the second results

The constant of proportionality is called the gain of the voltage divider. The value of the gain is determined by the resistance RA and RB (4)

Choosing the value of the resistors. It wasn’t possible to chose values…

The total resistance between any two points in a series circuit is equal to the sum of all the resistors connected in series between those two points.

In our simple circuit if the voltage source connected to a resistance Rx and Ry as shoen in figureâ€¦, for this circuit

If all the resistors in a series circuit are of equal value, the total resistance is the number of resistor multiplied by the resistance value of one resistor.

The total power in a resistive circuit is the sum of all the individual powers of the resistor making up the series circuit. Ground (Common) is zero volts with respect to all points referenced to it in the circuit. Negative ground is the term used when the negative side of the source is grounded. Positive ground is the term used when the positive side of the source is grounded. The voltage across an open component always equals to the source voltage. The voltage across a shorted component is always 0 V.

The circuit constructed was consisting of series string of resistors connected to a voltage source. Although there can be any number there are two voltage drop across the resistors: One across R1 and one across R2. These voltages drops are V1 and V2 respectively, as indicated iun the schematic. Since each resistor has the same current, the voltage drops are proportional to the resistance value. For example if R2 us twice of R1. Then the valye of V2 is twice that of V1. The total voltage drop around a single closed path divides among the series resistors in amounts directly proportional to the resistance value. The voltage divider is an important application of series circuits. This report will derive and apply the voltage-divider formula in order to obtain ratio of 2:1 between output voltages.

A series circuit can have only one path for current. The total resistance of a series circuit is found by the following equation:

Kirchhoff’s voltage law

Total power

If three equal resistors are used in a voltage divider, the voltage across each one will be one-third of the source voltage. A potentiometer can be used as an adjustable voltage divider.

The essential circuit of a voltage divider, also called potential divider is:

The voltage divider equation can be written as

The power dissipated by the resistor in a series circuit is the same as the power supplied by the source.

The theory applied to the circuit consists of a few calculation to develop a formula for determining how the voltage divided among series resistors.

The resistance between two terminals can be considered as one part and the resistance between other two terminals can be considered as another part.

The knowledge of how the filament lamp behaves under varying conditions of current and voltage is essential in building electronic circuits consists of the filament lamp therefore characteristic would be shown as a graph of the current (y-axis) versus voltage (x-axis) for the filament lamp. It will show how the electric current flowing through the component varies as the voltage across the filament lamp is gradually increases by the experimenter. The electric current in this experiment is the dependent variable i.e. it is dependent upon the voltage setting chosen by the experimenter.

## Assumptions statement

The resistors used in this experiment are given with a certain tolerance of 5%

The exact resistor values don’t matter, so long as their ratio is correct

The formula and the approximate rules given above assume that negligible current flows from the output. This is true if Vo is connected to a device with a high resistance such as voltmeter or an IC input.

## Experimental procedure and results

## Experimental procedure

## APPARTUS AND COMPONENETS

To carry the experiment the use of the following apparatus and components is required:

Breadboard

Black wire – to connect between the circuit and the negative supply terminal

Red wire – to connect between the circuit and the positive supply terminal

EL302Tv DC Power Supply – to supply DC voltage

MTX3240 5MHz Signal generator

TDS2002B digital oscilloscope – to measure the output AC voltage

Fluke 115 digital multimeter – to measure output DC voltage

Resistor Carbon Film 5% 0.25W brown-black-red-gold

Resistor Carbon Film 5% 0.25W brown-black-red-gold

Resistor Carbon Film 5% 0.25W brown-black-red-gold

Filament lamp T1.25 12V 30mA, bi-pin

2 Croc Clips

T-Piece

Electronics Test Probe

## REPERTORY OF METHODS

The set up of the apparatus needs to be done correctly and skilfully. The quantities measured are… Checking for errors in the measuring instruments and the need to take action should errors are found

This experiment begins with the three 1 kâ„¦ carbon film resistors with tolerance of 5% and power rating of 0.25W. Confirming the right resistors are used by comparing it with 1 kâ„¦ colour coding: Brown-Black-Red-Gold and measuring and recording their values as R1, R2 and R3

Connecting the two legs of the resistors in series on the bread board. Connect the bread board to the power supply and the multimeter as shown in figure …. the negative terminal of the power supply and the red probe to the positive terminal of the power supply to record the source voltage Vin, move the red probe to the terminal point A to record the voltage drop across R1.

To record the voltage across the “upper resistor” change the multimeter connection to the circuit as shown in figure…. noting the voltage drop across the other two resistors as V2

The main function of the 1 kâ„¦ resistor in this circuit is to control the current and the voltage across the lamp. If too much current flow through the filament lamp it is destroyed so the resistor is used to limit the current.

Connect the circuit on the bread board as shown if figure … below

Measure the source voltage, VS and the voltage across the filament, Vf for different Source voltage as shown in table 2. Calculate the current, If using Ohm’s law. Calculate the resistance of the filament Rf

Vs(V) Vr (V) IF=VR/R (A) VF(V) RF=VF/IF (Ohm)

2

4

6

8

## .

## .

## .

Table 3.1.2 I-V characteristics of a filament

Plot a graph of Vf versus IF and find the resistance of the filament at two points A and B specified below:

Resistance at A (Vf=1V), RA=

Resistance at B (Vf=3V), RB=

It is clear that the resistance at B is greater. This is because

## Results

[The results that appear in this section will be those on which the discussions will be based and from which the graphical plots will be represented. Results will normally have the units of the SI, although some may have traditional units, e.g. motor speed/rpm.]

Table 2 Amplifier gain as a function of frequency

‘from the measurements of input signal amplitude and output signal amplitude the voltage gain has been calculated as shown in Table 2’

Axes shall not have arrow heads at their ends, and division marks on an axis shall not be closer than 20 mm.

Data points should preferably be shown by small circles, squares or triangles with a dot in the centre; crosses, either vertical or inclined, may be used when all other options have been exhausted.

Do not use colour to differentiate between curves on the same figure; use different legends (e.g. circle and square) and perhaps different line types (e.g. continuous and broken). Give a legend key to describe the curves.

Keep a figure free from extraneous text and lines, such as a right angle and a calculation to determine a slope.

It would also help to show a thin lined grid.

## Discussion

## Interpretation of and/or commentary on the results

‘The discussion is the interpretation of and/or commentary on the results and the reasoning on which the conclusions are founded’.

For example, in a figure showing the variation of voltage gain of an amplifier with frequency might exhibit a slight increase in gain at high frequency before the main fall off in gain. Your text in the discussion should give reasons for this behaviour.

A variable resistor which can be varied by moving a knob or slider could also be used for this experiment. Connecting the pot’s three leg so it could act as a potential divider. Adjusting the potentiometer mechanism until the voltmeter register exactly 1/3 of total voltage between the wiper and the positive terminal and checking that this ratio maintain for double the voltage.

## Precision estimation

It is in the Discussion section that an estimate of the precision of your results should be given.

## Conclusions

‘The conclusions represents a clear and orderly presentation of the deductions made after full consideration of the results of the work. …….. the details of an involved argument or result should not be included’.

Making sure that the power ratings of the resistors are adequate for the application

Not all componenets obey Ohm’s law for the variation of current with voltage. Ohm’s law describes the behaviour of metals but even for these materials the law is only obeyed under very specific conditions of constant temperature and pressure. Thus Ohm’s law describes obly the behaviour of one type of material (metals) under very specific conditions.

The voltage divider is a very important basic circuit. The voltage divider is a very simple circuit that can be highly accurate if not loaded down. Understanding the principle of voltage divider helps in designing sensor systems and guide how to provide reference voltages to an electronic circuit in an analog-to-digital converter. use resistors in an appropriate configuration. low resistance values will draw a significant amount of current from the original source. This is probably acceptable if the original source is an electronic power supply, but not if it’s an actual battery. Thus, this use of a voltage divider is reasonable and appropriate in some circumstances, but not in all cases The proportionality of voltage drops (ratio of one to another) is strictly a function of resistance values. the voltage drop across each resistor is also a fixed proportion of the supply voltage.

The voltage divider is a very important basic circuit, and exploring the calculation above with various values can give you insight into a large number of practical circuit applications.

The ratio of individual resistance to total resistance is the same as the ratio of individual voltage drop to total supply voltage in a voltage divider circuit. This is known as the voltage divider formula, and it is a short-cut method for determining voltage drop in a series circuit without going through the current calculation(s) of Ohm’s Law.

Voltage dividers find wide application in electric meter circuits, where specific combinations of series resistors are used to “divide” a voltage into precise proportions as part of a voltage measurement device.

nn linear resistance thus Ohm’s law is only applicable at the linear band of the bulb resistance which is found to be 61.2â„¦.

conclusions about the work you did including any suggestions or modifications to the experiment

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