12th physics project

PHYSICS PROJECT TO DETERMING THE TIME CONSTANT ( FOR AN ‘RC’ CIRCUIT NIKHIL CHATURVEDI 12 - C ST. COLUMBA‟S SCHOOL ~1~

INDEX 1.Certification

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2.Acknowledgements

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3.General Introduction

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4.Experiment

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a) Aim

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b) Materials Required

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c) Theory

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d) Formulae Used

10

e) Circuit Diagram

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f) Procedure

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g) Graph

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h) Observations

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i) Calculations

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j) Result

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k) Precautions

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l) Problems Faced

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5.Bibliography

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CERTIFICATE This is to certify that Nikhil Chaturvedi of Cass XII-C of the academic year 2011-2012 has completed the project “TO DETERMING THE TIME CONSTANT ( FOR AN „RC‟ CIRCUIT” under my guidance and supervision and to my complete satisfaction.

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Mrs. N. Chatterjee ( Physics Teacher )

Mr. N. Prakash ( Lab Assistant ) ~3~

ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my Physics Teacher, Mrs. N. Chatterjee, and to our Lab Assistant, Mr. N. Prakash without the guidance of whom the completion of this project would not have been possible.

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General Introduction To The Project This project is based on the analysis of a simple RC circuit and how the voltages across its components vary with time. A resistor–capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit composed of resistors and capacitors driven by a voltage or current source. A first order RC circuit is composed of one resistor and one capacitor and is the simplest type of RC circuit. In this project, the focus is on slow RC circuits, the ones in which charging and discharging of the capacitor take place in a notable amount of time. This makes it possible for the human eye to observe the changes in the voltage and derive results from the readings. The various technical terms and formulae have been explained in detail in the project’s theory. The project aims to experimentally determine the time constant of an RC circuit and verify the results with existing formulae. Using the values obtained, the maximum charge on the capacitor shall be determined and the capacitor’s charging and discharging shall be represented graphically.

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EXPERIMENT Aim a) To experimentally determine the time constant of a slow RC circuit and verify the value using the actual formula. b) To calculate the maximum charge attained by the capacitor, i.e. the charge attained by it in steady state. c) To graphically represent the charging and discharging of the capacitor using the values obtained.

Materials Required  A Battery Eliminator of 10 V  An Electrolytic Capacitor of 100 F  A Carbon Resistor of 220 k  A Voltmeter  A Two-Way Switch  Connecting Wires  Stopwatch

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Theory I. Resistor :  A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element.  The current through a resistor is in direct proportion to the voltage across the resistor's terminals.  Thus, the ratio of the voltage applied across a resistor's terminals to the intensity of current through the circuit is called resistance.  The SI unit of resistance is Ohm (   This relation is represented by Ohm's law:

Where, R = Resistance V = Voltage across R I = Current through R

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II. Capacitor :  A capacitor (originally known as condenser) is a passive two-terminal electrical component used to store energy in an electric field.  The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric (insulator).  One common construction consists of metal foils separated by a thin layer of insulating film.  Capacitors are widely used as parts of electrical circuits in many common electrical devices.  The SI unit of Capacitance is Farad (F).  Capacitors are mainly of two types: Electrolytic capacitors and Non-Electrolytic capacitors.  The Capacitance of a capacitor is given by Where, C = Capacitance Q = Charge contained in C V = Voltage across C

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III. Types Of Capacitors : Non - Electrolytic Capacitors: Non-Electrolytic capacitors are non-polarized, i.e. they can be connected either way in a circuit without having to worry about + & -. The most common is the disc-type capacitor that we normally use in electronics. The other types are ceramic, mica etc. In almost all applications we use the disc-type capacitor which is brown in color and has the shape of a disc. Its value ranges between about a few pF to as high as 1uF.

Electrolytic Capacitors: Electrolytic capacitors are polarized and they are supposed to be connected in a specific way in the circuit. Their + and - terminals have to coincide with that specified in the circuit. They are much bulkier than the non-electrolytic type and hence have to be avoided when possible. They are used only if very high capacitance values are needed. Also the electrolytic capacitors are not very stable regarding their value i.e. their values change slightly with the temperature and other physical parameters. The nonelectrolytic capacitors are relatively more stable. Electrolytic capacitors are available usually 1uF and upwards up to about 4700uF. They are much costlier than the non-electrolytic capacitors. Connecting an electrolytic capacitor in the wrong polarity may lead to an explosion ~9~

Formulae Used Where,  = Time Constant of the circuit R = Resistance C = Capacitance

During Discharging, where, V(t) = Voltage at time t  = Voltage Supplied  = Time Constant

⁄

⁄

During Charging, where, V(t) = Voltage at time t  = Voltage Supplied  = Time Constant Where, V = Voltage after one Time Constant has passed during Discharging. ( t= ) Where, V = Voltage after one Time Constant has passed during Charging. ( t= )

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CIRCUIT DIAGRAM

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Procedure i. Obtain the components required for the circuit. ii. Clean the ends of the connecting wires with a sand paper. iii. Connect the +ve terminal of the battery eliminator E to the common end of two way switch S. iv. Connect the -ve terminal of E to the shorter leg of the electrolytic capacitor C. v. Draw a wire from the one of the ends of S and join it to the above wire to form a junction. vi. Connect a wire from the capacitor side of this junction to ground ( 0 Volts ). vii. Connect a wire from the longer leg of the capacitor to the resistor R. viii. Connect the other end of R to the remaining end of S. ix. Connect the Voltmeter, V, in parallel across C to complete the circuit. x. To start the experiment, turn S to the upper position and switch on E. Wait till the voltmeter reaches a steady value. Note that this value will be equal to 10V, the voltage provided by E. When this happens, the capacitor is said to be in steady state. xi. Once the capacitor is fully charged, turn S to the lower position and start the stopwatch. ~ 12 ~

xii. As the capacitor discharges through ground, the reading in V1 reduces gradually. As the reading in V reaches a value of E (.368), stop the stopwatch and note its reading. This is the value of one time constant. xiii. Turn S to the upper position again and start the stopwatch. xiv. Note the time when V displays a voltage of E (.632). This is the value of one time constant taken while charging. Both the observed values should be about the same. xv. Repeat discharging and charging three more times to get a total of 8 readings for the time constant. Note them in the observations table, and find their average to compute  xvi. Calculate the theoretical value of from RC and find the percentage error in computing the experimental  xvii. To find the maximum value of charge stored in C, multiply the voltage observed at steady state with the capacitance. xviii. Find the percentage error again after calculating the actual value from CE. xix. Repeat the charging and discharging processes to obtain the voltage values at 6 different time values for each. xx. Plot these on graph paper.

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Graph i. Take two graph sheets and mark voltage (in volts) along the y-axis, and time (in seconds) along the x-axis. ii. Plot the readings under charging in one and discharging on the other. iii. Join the plotted points with a smooth freehand curve. iv. Both the graphs should be exponential in nature.

Observations a) Instruments Used Voltage supplied = …………… V (d.c) Least Count of Voltmeter = ……………. V Least Count of Stopwatch = ……………. s Capacitance of Capacitor Used = ……………. F Resistance of Resistor Used = ……………. k ~ 14 ~

b) Table For Time Constant () -

S. No.

While

While

Charging

Discharging

(s)

(s)

Mean Value Of  (s)

1. 2. 3. 4. 5. 6.

Average Value Of  =

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……………. s

c) Table For Charging -

S. No.

1

2

3

4

5

6

4

5

6

Time (s) Voltage across V (V)

d) Table For Discharging -

S. No.

1

2

3

Time (s) Voltage across V (V)

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Calculations a) Percentage Error in  Experimental Value of t1 = ……………. s Actual value of R*C = t2 = ……………. s Difference in values = t = | t1 - t2 | = ……………. s Percentage Experimental Error =

= ……………. %

b) Maximum Charge in C Voltage across C in steady state = E = ……………. V Capacitance = C = ……………. F Maximum Charge Stored in C = C*E = ……………. C

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Result 1. Within Experimental Limits the Time Constant of the given slow RC circuit has been determined as …………. s, with a percentage experimental error of ……………. . 2. The Maximum Charge on the Capacitor has been determined as …………… C. 3. The charging and discharging of the capacitor were represented graphically and both the graphs turned out to be exponential in nature.

Precautions 1. The insulation from the ends of the connecting wires must be removed properly and the ends must be cleaned with sandpaper. 2. All connections must be ensured to be tight. 3. Readings involving the use of a stopwatch must be taken carefully and accurately.

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4. The polarities of all equipment used must be taken into account while connecting the circuit. 5. The Voltmeter must be connected in parallel across the Capacitor.

Problems Faced 1. In the first time, the capacitor was connected with reverse polarity and it became unusable! 2. A lag in the turning of the switch and the stopwatch was human and inevitable. 3. The exponential nature of charging and discharging made taking initial readings difficult.

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Bibliography  www.physics.umt.edu  Google Images  Wikipedia  Yahoo Images  www.scienceexp.com

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