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Electric Current in a Conductor Ohm's Law
OHM’S LAW:
"For a given conductor, at a given temperature the strength of electric current through it is directly proportional to the potential difference applied across it".
Let V be the potential difference applied across the conductor and I be the current flowing through it. According to Ohm's law,
i.e I\(\alpha\)V \(\Rightarrow\) I=\(\frac {1} {R}\)V
Note
a)Ohm's law is neither a basic law nor a deriavable one
b) Ohm's law is just an empherical relation.
c) Microscopically Ohm's law is expressed as J =\( nev_d \Rightarrow \)J=\( \sigma \)E
where \( \sigma \) is the electrical conductivity of the material -
Electric Current in a Conductor and Ohm's Law
VALIDITY (OR) LIMITATIONS OF OHM'S LAW:
a) Ohms law is valid only for linear conductors or ohmic conductors such as metals.
For linear or ohmic conductors, I versus V graphs are straight lines passing through origin as shown in A and B.
A)
slope= tan\(\theta\)=\(\frac {1}
{V}\)=\(\frac {1}
{R}\) =GB)
slope= tan\(\theta\)=\(
\frac{V}
{I} = R
\)
b) Ohm's law is not universal as it does not hold good in case of gases, crystal - rectifiers, thermionic valves, transistor, carbon, mica, vaccum tubes, thermistor and most of the electrolytes. The devices or substances which do not obey ohms law are called non- ohmic or non linear conductors.
For these I versus V graph is not a straight line but they are in a form of curves as shown for different materials.
Note
V = IR is applicable for all linear and nonlinear conductors but, ohm's law (V\(\alpha\)I) is not applicable for nonlinear conductors.
By drawing graph between voltage and current across conductors we observe that many conductors obey Ohm's law. Their resistance is called Ohmic resistance or linear resistance. But Ohm's law does not always hold good. If we replace the resistance wire by a torch bulb in an electrical circuit and note down values of current (1) for different voltages (V) then we see that the entire V-I graph drawn is not straight line (Fig.(a)).
For low values of V, it remains straight line and then becomes curved. For high voltage, current through the filament of the bulb becomes large so that the temperature of the filament of bulb becomes higher and higher as current increases in the filament. -
Electric Current in a Conductor and Ohm's Law
RESISTANCE:
Resistance of a specimen of a material is the opposition offered by it for the flow of current.
Definition: The resistance of a conductor is defined as the ratio of the potential difference 'V' across the condutor to the current 'i' flowing through the conductor.
Resistance R= \(\frac {V} {i}\)
Units of resistance: volt/ampere (or) ohm
Dimensional formula: \( ML^2 T^{ - 3} A^{ - 2} \)
The resistance of a specimen is said to be one Ohm if one Volt potential difference across it causes a current of one Ampere to flow through it.
1 ohm= \( \frac{{\text{1 volt}}} {{\text{l ampere}}} \)
Resistance of a conductor is a scalar quantity and is characterstic of the specimen as a whole. It depends on the nature of the material of the specimen, dimensions (length, area of cross section) of the specimen, and physical conditions like temperature, pressure and impurities.
Resistance is the bulk property of the conductor.
The below figures shows the symbols of fixed resistor and variable resistor.
Note
Cause of Resistance in a metalic conductor: When a potential difference is applied across a conductor, then electric field is set up in which free electrons gets accelerated. As a result, they collide against the ions and atoms and their motion is thus opposed. This opposition offered by ions and atoms due to collisions is termed as the resistance of the conductor. -
Electric Current in a Conductor and Ohm's Law
CONDUCTANCE:
The reciprocal of resistance (R) is called Conductance of a conductor, i.e
Conductance, G=\( \frac{1} {R}\)
The S.I unit of conductance is mho or siemen. Dimension formula of conductance is \( M^{ - 1} L^{ - 2} T^3 A^2 \)