TECHNICAL PHYSIC

BETE 1013 SEMESTER 1 SESI 2013/2014

LAB 4: OHM’S LAW AND FINDING THE RESISTANCE OF UKNOWN RESISTOR

LONG REPORT

DATE

NAME OF GROUP MEMBERS &MATRIX NUMBER 1. AMIRAH FARHANA BT ZAINAL (B071310961)

NAME OF INSTRUCTOR

1. ENGR. AHMAD SAYUTHI BIN MOHAMAD SHOKRI

2.

EXAMINER’S COMMENT VERIFICATION STAMP

TOTAL MARKS

FAKULTI TEKNOLOGI KEJURUTERAAN

UNIVERSITI TEKNIKAL MALAYSIA MELAKA

Tittle: OHM’S LAW AND FINDING THE RESISTANCE OF UKNOWN RESISTOR

Introduction of Ohm’s Law

Ohm's law states that the current through a conductor between two points is directly proportional

to the potential difference across the two points. Introducing the constant of proportionality, the

resistance one arrives at the usual mathematical equation that describes this relationship:

where I is the current through the conductor in units of amperes, V is the potential

difference measured across the conductor in units of volts, and R is the resistance of the

conductor in units of ohms. More specifically, Ohm's law states that the R in this relation

is constant, independent of the current.

The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827,

described measurements of applied voltage and current through simple electrical circuits

containing various lengths of wire. He presented a slightly more complex equation than the one

above (see History section below) to explain his experimental results. The above equation is the

modern form of Ohm's law.

In physics, the term Ohm's law is also used to refer to various generalizations of the law

originally formulated by Ohm. The simplest example of this is:

where J is the current density at a given location in a resistive material, E is the electric

field at that location, and σ is a material dependent parameter called the conductivity.

This reformulation of Ohm's law is due to Gustav Kirchhoff.

History of Ohm’s Law

In January 1781, before Georg Ohm's work, Henry Cavendish experimented with Leyden jars

and glass tubes of varying diameter and length filled with salt solution. He measured the current

by noting how strong a shock he felt as he completed the circuit with his body. Cavendish wrote

that the "velocity" (current) varied directly as the "degree of electrification" (voltage). He did not

communicate his results to other scientists at the time, and his results were unknown until

Maxwell published them in 1879.

Ohm did his work on resistance in the years 1825 and 1826, and published his results in 1827 as

the book Die galvanische Kette, mathematisch bearbeitet (The galvanic Circuit investigated

mathematically). He drew considerable inspiration from Fourier's work on heat conduction in the

theoretical explanation of his work. For experiments, he initially used voltaic piles, but later used

a thermocouple as this provided a more stable voltage source in terms of internal resistance and

constant potential difference. He used a galvanometer to measure current, and knew that the

voltage between the thermocouple terminals was proportional to the junction temperature. He

then added test wires of varying length, diameter, and material to complete the circuit. He found

that his data could be modeled through the equation where x was the reading from the

galvanometer, l was the length of the test conductor, a depended only on the thermocouple

junction temperature, and b was a constant of the entire setup. From this, Ohm determined his

law of proportionality and published his results.

Ohm's law was probably the most important of the early quantitative descriptions of the physics

of electricity. We consider it almost obvious today. When Ohm first published his work, this was

not the case; critics reacted to his treatment of the subject with hostility. They called his work a

"web of naked fancies" and the German Minister of Education proclaimed that "a professor who

preached such heresies was unworthy to teach science."The prevailing scientific philosophy in

Germany at the time asserted that experiments need not be performed to develop an

understanding of nature because nature is so well ordered, and that scientific truths may be

deduced through reasoning alone. Also, Ohm's brother Martin, a mathematician, was battling the

German educational system. These factors hindered the acceptance of Ohm's work, and his work

did not become widely accepted until the 1840s. Fortunately, Ohm received recognition for his

contributions to science well before he died.

While the old term for electrical conductance, the mho (the inverse of the resistance unit ohm), is

still used, a new name, the siemens, was adopted in 1971, honoring Ernst Werner von Siemens.

The siemens is preferred in formal papers.

In the 1920s, it was discovered that the current through an ideal resistor actually has statistical

fluctuations, which depend on temperature, even when voltage and resistance are exactly

constant; this fluctuation, now known as Johnson–Nyquist noise, is due to the discrete nature of

charge. This thermal effect implies that measurements of current and voltage that are taken over

sufficiently short periods of time will yield ratios of V/I that fluctuate from the value of R

implied by the time average or ensemble average of the measured current; Ohm's law remains

correct for the average current, in the case of ordinary resistive materials.

Ohm's work long preceded Maxwell's equations and any understanding of frequency-dependent

effects in AC circuits. Modern developments in electromagnetic theory and circuit theory do not

contradict Ohm's law when they are evaluated within the appropriate limits.

Objective:

1. To investigate the relationship between voltage, current and resistance.

2. To determine the resistance of unknown resistors.

3. To analyze data collected, reasoning in data interpretation and comprehensively summarize

all the findings.

4. At the end of the experiment, we will learn how to write a report based on the result and

questions given.

Theory

Ohm’s Law defines that voltage is proportional to the current and vice versa. The circuit current

is inversely proportional to the resistance, R, Current and voltage have a linear relationship with

resistance remain constant.

V α I

I α I/R

V=IR

Ohm’s law can be written in any of the following three ways depending on which of the

quantities is unknown:-

First, arrange the letters V, I, and R in a triangle like this:

I = V/R R = V / I V = IR

Electrical Power , (P) in a circuit is the amount of energy that is absorbed or produced within the

circuit. Unit is Watts (W).

First, arrange the letters V, I, and P in a triangle like this:

P = I V I = P/V V= P/I

Electrical current, I is the amount of charge passing by a given point in a conducting path

(circuit) per unit time. It is measured in Ampere, A.

Voltage or potential difference, V can be described as the energy required to move a unit of

charge through an element. The unit is Volt, V.

Resistance, R will limit or resist the flow of electric current in a circuit. It is measured in Ohm,

Ω.

The relationship between the voltage, current, and resistance is given by Ohm’s law.

Multimeter is a multifunction instrument since it can be used in measuring AC and DC voltage,

current and resistance. Voltage will be taken by connect the multimeter in parallel with the

resistor while current will be taken by connecting the multimeter in series with resistor.

Ohm’s Law pie chart.

From this pie chart, easy to understand and know to find Resistor, Current, Power and Volts.

Apparatus / Equipment:

1. On/Off Switch 1

2. Resistor (47Ω) 1

3. Resistor (100Ω) 1

4. Resistor (1 kΩ) 1

5. Resistor (4.7 kΩ) 1

6. Resistor (10 kΩ) 5

7. Connecting Wire (25cm), red 2

8. Connecting Wire (25cm), blue 2

9. Connecting Wire (50cm), red 1

10. Connecting Wire (50cm), blue 1

11. Power Supply 12V- / 6V~, 12V~ 1

12. Multi Range Meter 1

13. Milli ammeter (0-100 mA) 1

14. Voltmeter (0-3 V) 1

Procedure:

Part A

1. The circuit was set up as shown in the circuit diagram and the resistor 100Ω was insert as

Rx.

2. Voltage from the power supply were raised up from 3V up to 12V and were entered the

measured values for current intensity in Table 1 under “measured current intensity” column.

3. The resistance values were changed by following the order 100 Ω , 1k Ω , 47kΩ , 4.7kΩ ,

10kΩ and the voltage on the resistor were set as precisely as possible to 10V. The current

intensity were measured and entered the values in Table 2.

Circuit Diagram:

Part B

1. The circuit are connected in series as shown in Figure 2.

2. Close the switch and the value of I were recorded.

3. To find the value of Figure 3, the same procedure as 1 and 2. The current, I, were measured

and recorded for each combinations. The values of R and 1/I were included in the table.

4. Graph of 1/I against R/ohm were plotted. The gradient and y-intercept can be determined.

Circuit Diagram:

Figure 2

Figure 3

Result

Part A

Table 1

Resistance, R(Ω) Voltage, U(V) Current Intensity

measured, I (mA)

Current Intensity

theoretical, I (mA)

Current Intensity

theoretical, I (A)

100 3 30.89 30.00 0.03

100 6 63.05 60.00 0.06

100 9 96.03 90.00 0.09

100 12 124.48 120.00 0.12

Table 2

Voltage, U(V) Resistance, R(Ω) Current Intensity

measured, I (mA)

Current Intensity

theoretical, I (mA)

Current Intensity

theoretical, I (A)

10 47 226.67 212.77 0.213

10 100 107.53 100.00 0.100

10 1000 10.73 10.00 0.010

10 4700 2.20 2.13 0.002

10 10000 1.10 1.00 0.001

Part B

Resistance,

R(Ω)

Voltage,

U(V)

Current Intensity

measured, I (A)

Current Intensity

theoretical, I (A)

1/I (A)

10 3 0.250 0.300 4.00

15 3 0.150 0.200 6.67

20 3 0.140 0.150 7.14

25 3 0.100 0.120 10.00

30 3 0.090 0.100 11.11

40 3 0.062 0.075 16.13

Data Analysis:

Calculations for theoretical Part A:

Table 1

R constant = 100Ω

From Ohm’s Law, V=IR

To find current, I = V/R

1. When V = 3V

I = 3V/100 Ω

= 0.03 A @ 30mA

2. When V = 6V

I = 6V/100 Ω

= 0.06A @ 60mA

3. When V = 9V

I = 9V/100 Ω

= 0.09A @ 90mA

4. When V = 12V

I = 12V/100 Ω

= 0.12A @ 120mA

Table 2

V constant = 10V

From Ohm’s Law, V=IR

To find current, I = V/R

1. When R = 47 Ω

I = 10V/47 Ω

= 0.213A @ 212.77mA

2. When R = 100 Ω

I = 10V/100 Ω

= 0.100A @ 100.00mA

3. When R = 1000 Ω

I = 10V/1000 Ω

= 0.010A @ 10.00mA

4. When R = 4700 Ω

I = 10V/4700 Ω

= 0.002A @ 2.13mA

5. When R = 10000 Ω

I = 10V/10000 Ω

= 0.001A @ 1.00mA

Calculations for theoretical Part B:V constant = 3V

From Ohm’s Law, V=IR

To find current, I = V/R

1. When R = 10 Ω

I = 3V/10 Ω

= 0.300A @ 300mA

2. When R = 15 Ω

I = 3V/15 Ω

= 0.200A @ 200mA

3. When R = 20 Ω

I = 3V/20 Ω

= 0.150A @ 150mA

4. When R = 25 Ω

I = 3V/25 Ω

= 0.120A @ 120mA

5. When R = 30 Ω

I = 3V/30 Ω

= 0.100A @ 100mA

6. When R = 40 Ω

I = 3V/40 Ω

= 0.075A @ 75mA

To find 1/I:

1. When R = 10 Ω

I = 0.250A

1/I = 1/0.250 A

= 4.00A

2. When R = 15 Ω

I = 0.150A

1/I = 1/0.150A

= 6.67A

3. When R = 20 Ω

I = 0.140A

1/I = 1/0.140 A

= 7.14A

4. When R = 25 Ω

I = 0.100A

1/I = 1/0.100 Ω

= 10.00A

5. When R = 30 Ω

I = 0.090A

1/I = 1/0.090

= 11.11A

6. When R = 40 Ω

I = 0.062A

1/I = 1/0.062A

= 16.13A

Graph of 1/I against R/ohm:

= 14-4 = 10

36-10 26

= 0.4

Discussion:

y-intercept = 0

For this experiment, we have done two part that are Part A and Part B. In part A section,

we need to set the circuit diagram where the resistor value of 100Ω is connected in series to the

ammeter and parallel to the voltmeter. The same value of resistor are connected to the power

supply for different voltage value that are from 3v to 12v to find the value of current of each

voltage. So that the value of current intensity can be measured and recorded in Table 1. For table

2, the value of voltage is constant where it used 10V and the value of resistor used are different

that are 47Ω, 100Ω, 1000Ω, 4700Ω, and 10000Ω to find the value of current intensity and the

value were recorded. After that, we apply Ohm’s Law where V=IR for the theoretical

calculations to compare the value that we had measured in the experiment. Based on the result

obtained, there a slightly difference value between the theoretical and practical value. This is due

of some factor that may affect the results. For instance, the value of resistor used is not exactly

same original value because the resistor is used many times. If the resistor is in series with the

circuit, it will impede the flow of current, decreasing the current into the circuit. If the resistor is

in parallel with the circuit, that added resistor will provide another path for current thus

increasing the current out of the voltage supply but not effecting the current into the circuit since

the supply voltage is independent of current which means the circuit would see the same voltage

across it. Besides that, factors that can affect accuracy would involve using incorrect amounts,

incorrect procedures, impure substances, or anything that does not follow the correct procedure.

From the results table obtained in part B, it can be observed that the value of currents

from the experiment was slightly different from the theoretical calculations. This is also due of

the resistance used. In theory, the resistance is neglect because it was very small value but when

it in practical it can affect the result. In addition, the multi range meter used is in 1 decimal

places and thus it cannot give an accurate value compare the theoretical value. Last but not least,

when measured the current intensity for resistance 10Ω, voltage 3V it cannot be measured and

give undefined value. This is because the voltage were too high and multi range meter only can

be reading in maximum value of 0.3A. So, as the result the resistance is burned.

Resistors in series is when two or more resistors are connected together end-to-end in a

single branch. Resistors in Series carry the same current, but the potential differences across

them is not the same as their individual resistance values will create different voltage drops

across each resistor as determined by Ohm's Law ( V = IxR ). In a series resistor network the

individual resistors add together to give the equivalent resistance, ( RT ) of the series

combination. The resistors in a series circuit can be interchanged without affecting the total

resistance, current, or power to each resistor or the circuit.

Resistors in parallel is when two or more resistors are connected so that both of their

terminals are respectively connected to each terminal of the other resistor or resistors, they are

said to be connected together in parallel. The potential differences across each resistor in the

parallel combination is the same but the currents flowing through them are not the same.The

equivalent or total resistance, RT of a parallel combination is found through reciprocal addition

and the total resistance value will always be less than the smallest individual resistor in the

combination. Parallel resistor networks can be interchanged within the same combination

without changing the total resistance or total circuit current. Resistors connected together in a

parallel circuit will continue to operate even though one resistor may be open-circuited.

Conclusion:

After we finish do our first practice, we have known, Ohm's law states that an electric

current, I flowing view of his training of a conductor between two other points is proportional to

the potential difference, V between the two points, and inversely proportional to the resistance,

relation between current, voltage and resistor. After that, when we constant the value of voltage

supply, it have different at output of the current when use to manipulate the resistor. Same goes

if we change the value of the supply voltage and constant the value of resistor value and we get

the change of current value. So, we can conclude that the relation between the resistor, voltage

and current. The objective of the experiment is achieve.

References:

Internet-:

http://en.wikipedia.org/wiki/Ohm's_law

http://utwired.engr.utexas.edu/rgd1/lesson01.cfm

http://www.angelfire.com/ri/dcvoltage/theory.html

http://www.the12volt.com/ohm/ohmslaw.asp

http://www.allaboutcircuits.com/vol_1/chpt_2/1.html

http://www.electronics-tutorials.ws/resistor/res_3.html

Journal-:

Ohm's Law Electrical Math and Voltage Drop Calculations By: Tom Henry

Fundamental of Electric Circuits By Charles K.Alexdender and Matthew N.O. Sadiku

Physics for Scientists & Engineers with Modern Physcis By: Douglas C.Giancoli