Electric Circuits And Currents

Electric Circuits And Currents
 

INTRODUCTION
The flow of water in a river constitutes a current of water. Flow of heat in a conductor is called thermal current. Similarly flow of charges i.e., charges in motion constitute electric current. We have seen in Electrostatics that when an isolated conductor is placed in an electric field, the charges in the conductor rearrange themselves so that the interior of the conductor has no net electric field. The rearrangement of charges constitutes a current of short duration, called a transient current. The transient current ceases, the moment the net electric field in the conductor becomes zero. Another example of transient current is when we see lightening, which is the flow of electric charge between two clouds or from a cloud to the earth. But we are also familiar with continuous steady currents, such as in a battery torch. The current goes on as long as the torch is on (if the battery has not run out of use!) producing heat in the bulb and light.
How does one maintain such a steady current? In this chapter, we look into the essential require- ments for maintaining a steady current a source of emf, as it is called. We also introduce the concept of resistance and attempt to understand it by a qualitative microscopic picture. Finally, we describe the basic laws (kirchoff's rules) governing electric current and their applications.
basic laws (kirchoff's rules) governing electric current and their applications.

STRENGTH OF ELECTRIC CURRENT:
The strength of electric current is defined as rate of flow of charge through any cross section of a conductor.
If a net charge 'Q' passes through any cross section of the conductor in time 't' then the average current 'I' is given by
        Average current I=\( \frac{Q} {t} \)  
Current is a scalar quantity. It is a macroscopic quantity like the mass of a body or volume of a container. In SI Units, current is one of the fundamental physical quantities. It is
dimensionally denoted by [I] or [A].
The direction of current is the direction of flow of positive charge (or) opposite to the direction of flow of negative charge.

Ampere: If one coulomb of charge passes through a cross-section of the conductor per second then the current is one ampere.
            Ampere(A)= \( \frac{{\text{coulomb (C)}}} {{\text{second}(s)}} \)
An ampere is typically the order of magnitude of currents in domestic appliances. An average th lightning carries currents of the order of tens of thousands of amperes and at the other extreme, currents in our nerves are in microamperes.

Note:
If n particles, each having a charge q, pass through a given cross sectional area in time t, then average current is i=\( \frac{{nq}} {t} \)

Note-:
If in a discharge tube  protons are moving from left to right in t seconds and  electrons are moving simultaneously from right to left in t seconds, then the net current in any cross section of the discharge tube is
            I=  \( \frac{{\left( {n_1 + n_2 } \right)e}} {t} \) (from left to right)
here e is the magnitude of charge of electron (or) proton.

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:
 V = IR is applicable for all linear and nonlinear conductors but, ohm's law (V \( \alpha \) I) is not applicable for nonlinear conductors.
    
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 

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.

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. 

RESISTIVITY:
As we know, that the resistance of the conductor is directly proportional to its length and inversely proportional to its area of cross section, we can write
           \( R\alpha \frac{1} {A} \Rightarrow R = \frac{{\rho l}} {A} \)
        
where \( \rho \) is specific resistance or resistivity of the material of the conductor.
Now, let us define the specific resistance of the conductor.
If l = 1 m, A = 1_m² , then \( \rho \) = R.
The resistance of a conductor of unit length and unit area of cross section is called specific resistance or resistivity of the material of the conductor.
SI unit of specific resistance: ohm-m  
A perfect conductor would have zero resistivity, and a perfect insulator would have an infinite resistivity. Metals have low resistivities in the range of 10-8-m to 10-60-m have the smallest resisti- vities and are the best conductors. The resistivities of insulators are greater than those of the metals by an enormous factor, of the order of  \( 10^{ - 8} \Omega - m \) to \( 10^{ - 6} \Omega - m \)

POINTS TO REMEMBER:
1. Resistivity is the specific property of a material but Resistance is the bulk property of a conductor
2. Resistivity is independent of dimensions of the condutor such as length, area of the cross section.
3. Resistivity depends on the nature of the material of the conductor, temperature and impurities. 
4. Resistivity of metals increases by the addition of impurities. Resistivity of any alloy is more than the resistivity of its constituent elements.
For example,constantan, manganin and nichrome have high resistivities as compared to their constituent metals.
5. Silver, copper and aluminium have very low values of resistivity, so they are used in the manufacture of electric cables and connecting wires.
6. Fuse wire is made of tin-lead alloy. It should have low melting point, low resistivity.
7. The elements of heating devices are made up of nichrome which has high resistivity and high melting point 
8. The filament of electric bulb is made up of tungsten which has low resisvity and high melting point.
9.  At absolute zero resistivity of any metal becomes zero \(\to\) (super conductor) any semiconductor becomes infinity \(\to\) (perfect insulator)