dear meitnation can u please explain it mathematically using the ohms law. also show the graph.?

Good answer @ roshri!

@Alisha: Please look at the circuit diagram and the graph and the explanation along with them to understand how to plot the V-I graph.

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Ohm’s law states that the current flowing through a conductor is directly proportional to the potential difference across the conductor. The proportionality constant is the resistance of the conductor, it is a constant for a known temperature range.

 

An activity:

Connect the wires as shown in the diagram. Increase the rheostat to increase the current in the circuit, obtain the value of current in the circuit by the ammeter and also find the potential difference using the voltmeter. For increase in current see the brightness of the bulb connected. Use your knowledge so far to obtain the resistance of the bulb.

 

Graph of Ohm’s law is a straight line obtained when current in the circuit (I) is plotted along x axis and potential (V) along y axis.

Current is given by Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/wgsgpexa1855634074631969365.gif -----------1.

Current I = current, n = no. of electrons per unit volume, A = CSA of the conductor, v = drift velocity, e = electronic charge, E = Electric Field strength, Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/ssqgzdoy8473869548757715680.gif = mass of electron, F = force, a = acceleration

Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/pcxedvzl8364060165610464145.gif

Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/uohelfqi3472180311581679404.gif ------------2.

Again, Potential (V) is given by

Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/tifattaf9156145112192820845.gif

Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/ixtwbrcw906200841732510098.gif ------------3.

By 2 and 3

Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/mzmvfrdc6868952428571139645.gif --------4.

 

where l = length of the conductor

Normally, due to electric force the charges should accelerate, but it does not accelerate due to repeated collisions with the +ve kernels. The path between two successive collision is called the free path Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/sreimcql1260849859070099327.gif ( Thus the charges have an average velocity called drift velocity v.

Thus, Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/sreimcql1260849859070099327.gif is given by,

Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/uqujskvi5722941511782079225.gif where t = average relaxation time (i.e. free time without a collision)

Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/xqoswsax6667187820324715506.gif

Or, Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/vcsokgcf1856271887772125481.gif -----------5.

 

By 4 and 5

Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/bmrhpdfv8482059738642330164.gif ------------6.

 

 

By 1 and 6

Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/apaxdent5087809251281347126.gif

Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/apaxdent5087809251281347126.gif

Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/nekgfjrx2272963499888370888.gif

Description: /img/shared/discuss_editlive/2191102/2012_01_06_00_08_32/dbonyule5211813742898210772.gif

Now mass of electron m, length of the conductor l, charge of electron e, CSA of conductor A, relaxation time t (constant for a given temperature). Thus

VαI (T remaining constant)

Which is Ohm's law

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Ohm’s law states that the current (I) flowing through a conductor is directly proportional to the potential difference (V) across the ends of a conductor, provided physical conditions of the conductor such as temperature, mechanical strain etc. are kept constant.
V I
On removing the proportionality signs we get:
V = IR
Where R is the resistance and is measured in SI unit called ohm(Ω).
Since according to ohm’s law V is directly proportional to I , Therefore the graph has to be a straight line. This straight line hence also indicates that Resistance is a constant quantity throughout.

.

 

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Ohm’s Law:

This law states that the ratio of potential difference between the ends of a conductor to the current flowing through the conductor is a constant. This constant is defined as Resistance of the conductor.

Or V=I R

Or R=V/I

Where R=Constant (Resistance)

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thnx roshri but i wanted 2 know how to make the vi graph!!

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