Ohm\'s Law Lab 1) What Was Your Value For The Slope... PDF

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Ohms Law lab physics 2049 lab, MDC , su mmer 2021...

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5/25/2021

Ohm's Law Lab 1) What Was Your Value For The Slope... | Chegg.com

General guidance Concepts and reason The concepts used to solve this question are Ohm’s law, slope of a line, possible errors in Ohm’s law experiment and percentage error. Initially, determine the slope of the Ohm’s law graph and unit of the slope by using the formula of Ohm’s law. Then, determine the unit of the slope of the Ohm’s law graph and its physical significance by using the relation between voltage and current. Later, determine the percentage error in the slope of Ohm’s law graph, by using the formula for percentage error. Then, the possible errors in Ohm’s law graph are analyzed and we need to comment on the sources of these errors. Finally, determine the physical significance of intercept by using Ohm’s law and use the concepts of Ohm’s law to comment on the effect of voltage when the circuit was turned off.

Fundamentals Ohm’s law: Ohm’s law gives a relation between the current and voltage flowing through a circuit. It states that at a constant temperature, the current flowing through the conductor is directly proportional to the voltage across it. Mathematically it can be expressed as,

Here, is the voltage across the circuit, is the current flowing through the circuit and is the resistance of the circuit. Constant of proportionality is the electrical resistance between the ends of the conductor. Unit of voltage is in Unit of current is in Unit of resistance is . If the temperature of the conductor is varying then Ohm’s law will not hold.

Figure:1 shows the variation of voltage with the current at a constant temperature. Slope of a line is the ratio of change in coordinates in the and axis directions. The slope of the line depicted in the graph can be determined by using,

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Here, is the slope of the line in the voltage current graph, is the change in voltage and is the change in current. Errors in experimental measurements: Errors in measurements are generally classified into two, 1.Systematic error 2.Random error Systematic errors are those errors that normally tend to either positive or negative direction. Causes of systematic error include, • Instrumental error • Imperfection in the experimental procedure • Personal error The instrumental error arises due to the zero error in the instrument, imperfect design and calibration of the instrument. Imperfection in experimental procedure includes the change in the experimental procedure. Personal error is due to the improper setting of the instrument due to the carelessness of the individual. It can also be called as human error. Random errors occur irregularly due to the unpredictable change in the experimental conditions like temperature variation, voltage supply, etc. Percentage error: The relative error is the ratio of error to the value of the quantity measured. Error is the difference in the values of approximated value and true value. Mathematically it can be expressed as,

Here, is the error value, is the value of resistance from the linear Ohm’s law graph i.e. value in which we have measured approximately. The value is is the difference in the resistance value from the linear Ohm’s law graph and the true value of resistance from the experiment. The true value of resistance from the experiment is calculated from the tolerance value of the slope given. Mathematically it can be expressed as,

Here,

is the true value of resistance from the experiment.

Value of is the mean of maximum and minimum resistance value calculated using the given tolerance value of the slope. Percentage error is the relative error expressed in percentage. Mathematically percentage error is expressed as,

Here,

is the percentage error in resistance. Show less

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Step-by-step

FIRST STEP|ALL STEPS|ANSWER ONLY

Step 1of 6 (1.1) The slope of the Ohm’s law graph can be calculated by evaluating any two points in the linear fit data of the Ohm’s law graph. From the linear fit data, we will only get the value of the approximated slope of Ohm’s law graph. Consider the points as origin

and

The slope of the graph can be mathematically expressed as,

Substitute

for

and

for

The value of the slope of the Ohm’s law graph is

.

Part 1.1 The value of the slope of the linear fit Ohm’s law graph is

.

Explanation|Common mistakes|Hint for next step Slope of the voltage-current graph can be determined by taking the ratio of the change in voltage and change in current. Mathematically it can be expressed as,

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Step 2of 6 (1.2) The slope of Ohm’s law graph is obtained as,

Unit of voltage is in , unit of current is in Unit of the slope of Ohm’s law graph is expressed as,

,

Here, S is Siemens. SI unit of electrical resistance is ohm. The ohm is defined as the electrical resistance between the two ends of a conductor when a constant potential difference of one volt applied to ends produces a current of one Ampere in the conductor. So the unit of the slope of Ohm’s law graph is ohm. The physical quantity represented by the slope of Ohm’s law graph is electrical resistance. The opposition to the flow of electric current is the electrical resistance. So the unit of the slope of the Ohm’s law graph is ohm. Part 1.2 Unit of the slope of the Ohm’s law graph is ohm.

Explanation|Common mistakes|Hint for next step Ohm’s law, states that at constant temperature the voltage across the current carrying conductor is proportional to the current flowing through it. The slope of the Ohm’s law graph will give the electrical resistance between the ends of the conductor. SI unit of electrical resistance is ohm.

Step 3of 6 (2.1) The relative error is the ratio of error in measurement to the value of the quantity measured. Error is the difference in the values of approximated value and true value. Mathematically it can be expressed as,

The value is is the difference in the resistance value form the linear Ohm’s law graph and the true value of resistance from the experiment. Percentage error can be calculated using,

From the given data we can find the tolerance zone of electrical resistance.

The upper limit for resistance will be Taking the mean value of resistance,

and the lower limit for resistance

will be

.

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Substitute

for

and

for

Percentage error can be calculated by,

Here,

is the error in the resistance value and

Substitute

Substitute

for

for

and

and

is the resistance value from the linear fit data.

for

for

The percentage error calculated from the slope to the accepted value will is

.

Part 2.1 The percentage error calculated from the slope to the accepted value will is

Explanation|Common mistakes|Hint for next step The relative error is defined as the ratio of mean absolute error to the mean value of the quantity measured. Mathematically it can be expressed as,

Percentage error is the relative error expressed in percentage.

Step 4of 6 (2.2) Errors in Ohm’s law experiment are analyzed as, 1.Systematic error 2.Random error The practical observation of the Ohm’s law will never match with the theoretical readings. Systematic error may be the main reason for the error in Ohm’s law.

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There is some tolerance value for the carbon and metallic film resistors. They usually have a tolerance value of . So the value of actual current and voltage will vary from the theoretical value. Ohm’s law holds good when the temperature of the current carrying conductor is at a constant temperature. Any temperature variation in the current carrying conductor may not hold the Ohm’s law validity. Temperature variation is also a random error which occurs due to the unpredictable change in the experimental conditions. Part 2.2 The possible sources for the error in reading of Ohm’s law graph will be due to systematic and random errors.

Explanation|Common mistakes|Hint for next step Error in Ohm’s law is mainly due to systematic and random errors. Systematic error is due to the tolerance limit of the resistor material while the random error is due to the temperature variation of the current carrying conductor.

Step 5of 6 (3.1) The intercept in Ohm’s law graph is voltage. Voltage is the difference in electric potential between two points in a current carrying conductor. The difference in voltage between two points in an electric field is defined as the work needed per unit charge to move the charge between the two points. SI unit of voltage is volt

.

Part 3.1 The physical meaning of

intercept is potential difference.

Explanation|Common mistakes|Hint for next step Voltage is the electric potential between two points in a current carry conductor. Ohm’s law explains the relationship between electric potential and the current flowing through a current carrying conductor.

Step 6of 6 (3.2) Voltage is the difference in electric potential between two points in a current carrying conductor. Open circuit voltage is the difference in electrical potential between the terminals when the circuit is disconnected. Also, no electric current flows between the terminals of the circuit. Even though the circuit is not connected to any load but still the potential of the system exists. Part 3.2 The value of electric potential was detected in the circuit after disconnecting is due to the open circuit voltage.

Explanation|Common mistakes Voltage is the electric potential between two points in a current carry conductor.

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Ohm’s law explains the relationship between electric potential and the current flowing through a current carrying conductor. The difference in voltage between two points in an electric field is defined as the work needed per unit charge to move the charge between the two points. SI unit of voltage is volt . Open circuit voltage is the electric potential of the circuit after the circuit is not connected to the load.

Answer Part 1.1 The value of the slope of the linear fit Ohm’s law graph is

.

Part 1.2 Unit of the slope of the Ohm’s law graph is ohm. Part 2.1 The percentage error calculated from the slope to the accepted value will is Part 2.2 The possible sources for the error in reading of Ohm’s law graph will be due to systematic and random errors. Part 3.1 The physical meaning of

intercept is potential difference.

Part 3.2 The value of electric potential was detected in the circuit after disconnecting is due to the open circuit voltage.

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