“To measure the attenuation by varying separation between plates of Parallel Plate Capacitor”

 “To measure the attenuation by varying separation between plates of Parallel Plate Capacitor”

1          Objective:

The objective of this experiment is

        i.            To find dielectric constant of water
      ii.            To study variation in dielectric constant by varying separation between plates

2          Abstract:

In this experiment dielectric of water is measured by varying the separation between the plates. Input is given with the help of an oscillator. Waveform is seen on Cathode Ray Oscilloscope and output is measured.

3          Introduction/Literature Background:

3.1.Capacitor:

 “A capacitor is a device that stores energy in an electric field, by accumulating an internal imbalance of electric charge.”

3.2.Explanation:

A capacitor can be "charged" and can store charge. when a capacitor is being charged, negative charge is removed from one side of the capacitor and placed onto the other, leaving one side with a negative charge (-q) and the other side with a positive charge (+q). The net charge of the capacitor as a whole remains equal to zero.

3.3.Parallel plate capacitor:

When two parallel plates are connected across a battery, the plates will become charged and an electric field will be established between them.

 Remember that the direction of an electric field is defined as the direction that a positive test charge would move. So in this case, the electric field would point from the positive plate to the negative plate. Since the field lines are parallel to each other, this type of electric field is uniform and is calculated with the equation E = V/d.

 The capacitor can be charged by connecting one plate to the positive terminal of a battery and the other to the negative terminal. The electric field produced by the battery causes electrons to flow towards the positive terminal of the battery and away from the negative terminal. This causes the two capacitor plates to become charged. One will be positively charged and the other will be negatively charged. The insulating material keeps the charges from crossing over from one plate to the other and allows the capacitor to store electrical energy. If it is disconnected from the battery, the charges will remain stored in the capacitor until it is connected to another electric unit.

3.4.Capacitance:

“Capacitance is a measure of a capacitor’s ability to store charge.”

Capacitance is a constant of proportionality. It relates the potential difference v between two conductors to their charge, q. the charge q is equal and opposite on the two conductors. The relationship can be written:

Q = CV

The capacitance C of any two conductors depends on their size, shape, and separation. One of the simplest configurations is a pair of flat conducting plates, which is called a “parallel-plate capacitor.” theoretically, the capacitance of parallel-plate capacitors is

C_P = Epsilon A/d

where the subscript “p” denotes “parallel plate.” here, a is the area of one of the plates, d is the distance between them, and ε₀ is a constant called the “permittivity of free space,” which has a value of 8.85 × 10^-12 c² / n-m², in SI units. A typical capacitor consists of two conducting surfaces (usually metal plates) separated by an insulating material like air, rubber, or paper. This insulating material is called a dielectric

3.5.Effect of dielectric:

Most capacitors have an insulating (or dielectric) material between the plates. The presence of this dielectric increases the capacitance of the capacitor compared to when the space between the plates was empty (a vacuum).The insertion of a dielectric between the plates of a capacitor causes the potential difference V_O between the plates to decrease to V. the original capacitance, from

Q = CV,

Is given by

C_O = Q / V_O

And since q must stay constant we have

C_OV_O = CV,

And if V_O decreases to V, C_O must increase to C to keep the equation balanced. And since

V = Ed,

We can conclude that the electric field between the plates must be reduced as a dielectric is inserted q = (constant).The capacitance can be written as

C=C_med = Epsilon A/d

Where Epsilon is dielectric constant. Which is equal to the ratio of capacitance when dielectric is inserted to the capacitance without air.

3.6.Capacitors in DC Circuit:

Capacitors do not play an important role in DC circuits because it is impossible for a steady current to flow across a capacitor. If an uncharged capacitor C is connected across the terminals of a battery of voltage V then a transient current flows as the capacitor plates charge up. However, the current stops flowing as soon as the charge Q on the positive plate reaches the value Q=CV. At this point, the electric field between the plates cancels the effect of the electric field generated by the battery, and there is no further movement of charge. Thus, if a capacitor is placed in a DC circuit then, as soon as its plates have charged up, the capacitor effectively behaves like a break in the circuit.

A capacitor blocks DC as once it gets charged up to the input voltage with the same polarity then no further transfer of electrons can happen accept to replenish the slow discharge due to leakage if any. Hence the flow of electrons which represents electric current is stopped. The capacitor in the drawing on the left is charging from a voltage supply Vs provided by the battery. Initially the voltage on the capacitor will be 0V and the voltage on the resistor will be Vs. this means that the current through Vs is at a maximum as it is determined by Vs/R. The capacitor begins to build a charge and the equation for a voltage on a capacitor is 

V_c= Q/C

Where Q is the charge.

As Vc increases, Vs gets smaller, and therefore the current through the resistor gets smaller too (I=V/R). As the current is doing the charging, the rate of charge of the capacitor is slowed down.

3.7.Capacitor in AC Circuit:

DC has zero frequency, so reactance is infinity. This is the reason DC is blocked. While AC has some frequency, due to which capacitor lets it flow.

A purely capacitive AC circuit is one containing an AC voltage supply and a capacitor. The capacitor is connected directly across the AC supply voltage. As the supply voltage increases and decreases, the capacitor charges and discharges with respect to this change. A current will flow through the circuit, first in one direction, then in the other. However, no current actually flows through the capacitor. Electrons build up on the one plate and are drained off from the other plate in very rapid succession, giving the impression that the current flows through the insulator separating the plates.

3.8.Uses of capacitors:

Capacitors are used in many devices that require electrical energy to be released quickly, like camera flashes and computer keyboards. A simple, everyday use of capacitors is in the flash unit for a camera. You need a large charge in a very short time to light up the camera's flash bulb. The camera's battery cannot provide such a large charge in such a short time. So the charge from the battery is gradually stored in a capacitor, and when the capacitor is fully charged, the camera lets you know that it's ready to take a flash picture.

 They are also used in circuits that are designed to filter and amplify electronic signals. These circuits are found in radios, music amplifiers, and medical devices.

3.9.Cathode Ray Oscilloscope:

The cathode ray oscilloscope is an instrument which we use in laboratory to display measure and analyse various waveforms of various electrical and electronic circuits. Actually cathode ray oscilloscope is very fast X-Y plotters that can display an input signal versus time or other signal. Cathode ray oscilloscope uses luminous spot which is produced by striking the beam of electrons and this luminous spot moves in response variation in the input quantity. The reason behind the use of an electron beam is its low effect that can be used for following the changes in the instantaneous values of rapidly changing input quantity. The general forms of cathode ray oscilloscope operate on voltages. So the input quantity that we have talked above is voltage. Nowadays, with the help of transducers it is possible to convert various physical quantities like current, pressure, acceleration etc to voltage thus it enable us to have a visual representations of these various quantities on cathode ray oscilloscope.

4.     Apparatus:

                    i.            Parallel Plate Capacitor

                  ii.            Water Bag

                iii.            Cathode Ray Oscilloscope

                iv.            Signal Generator (AC Source)

                  v.            Connecting Wires

                vi.            Probes

              vii.            Digital Multi meter

5.     Experimental Setup:

6.     Experimentation

1.      Connected the circuit as shown in circuit diagram and switch on the power supply.

2.      Noted the distance d between the plates of a capacitor.

3.      Input frequency given through signal generator is noted.

4.      Input Voltage is measured by digital multi meter

5.      Capacitor is charged during positive half cycle of A.C. source.

6.      A corresponding wave form is observed on C.R.O.

7.      No. of horizontal divisions is counted and sweeps time per division reading is noted from CRO.

8.      Time period is calculated by

no. of horizontal divisions × Sweeps time per division

9.      Calculated output frequency from C.R.O. by

Frequency=

10.  Calculate Output Voltage i.e Peak to Peak Voltage from C.R.O. by

Volts per division × Number of Vertical Divisions

11.  Calculate V_rms using the formula,

12.  Measured attenuation using the formula:

A_v = 20log

13.  Now finally calculated the value of dielectric constant using the formula,

14.  Repeat the experiment by varying the distance between the plates and measure dielectric constant.

7.     Observation & Calculation:

No. of Obs.	Distance (d) cm	Output Frequency	Output Voltage	r.m.s value of Voltage	Attenuation	Dielectric constant
	(Hz)	(Hz)			20log
1	13
2	17
3	33

8.     Results & Discussion:

AC can flow easily through capacitors, but DC is blocked when capacitor is fully charged.AC flow because of alternating current reverses direction. As in this experiment we measured dielectric constant of water by using parallel plate capacitor, here are something to be noted that are the effect of distance, area etc. on capacitance. The increase in distance between the plates decreases its ability to store charge, but increase in area increases its capacitance which affects the value of constant measured. It can be concluded that “decreasing the separation between the plates, decreases the voltage and frequency as they directly relate with separation between plates but dielectric constant increases which shows that increased distance allows capacitor to increases its capacitance hence its dielectric constant increases.

9.     References:

·         http://www.physics.sjsu.edu/becker/physics51/capacitors.htm

·         http://study.com/academy/lesson/what-is-capacitance-definition-equation-examples.html

·         http://www.thebigger.com/physics/electrostatics/what-are-parallel-plate-capacitors/

·         http://farside.ph.utexas.edu/teaching/302l/lectures/node60.html