DIRECT CURRENT

DIRECT CURRENT

The current, I is defined as the net amount of charge per unit time through an area perpendicular to the flow direction 

SI unit of current is Coulomb per second, C/s or Ampere, A

The direction of electric current is defined as the direction of positive charge transported. For example, if electrons (negative charge) move to the left, the positron (positive charge) moves to the right (opposite direction)

CURRENT AND DRIFT VELOCITY

In absence on an applied electric field, the conduction electrons in a conductor are in constant random motion at high speed. The electrons suffer frequent collisions with each other and with ions. A collision can change the direction of the electron’s motion so the electron moves in random path. The average velocity of the conduction electrons is zero in the absence of an electric field so there is no net transport of charge.

If uniform electric field exists within a conductor, the electric force on the conduction electrons gives them a uniform acceleration between collisions. The electrons still move about in random directions but the electric force makes them move on average a little faster in the direction of the force than in opposite direction. As a result, the electrons slowly drift in the direction of the electric force. The electrons now have a nonzero velocity called drift velocity, 

Figure 1: Free an electron moving in a conductor make many collisions with other electrons and atoms. The average velocity of the free charges is called the drift velocity,  and it is in the direction opposite to the electric field for electrons. The collisions transfer energy to the conductor, requiring a constant energy to maintain a steady current.

 The number of conduction electrons per unit volume (n) is a characteristic of a particular metal. Suppose calculate the current by finding how much charge moves through the shaded area in a time,. During that time, every electron moves a distance  to the left. Thus:

The number of electrons in conductor, 

The magnitude of the charge,

Figure 2: The conduction electrons moving at uniform velocity in a time 

with an electron moves a distance

Therefore the magnitude of the current in the wire,

Also can define current density, j

The current density, j is defined as the electric current, I per unit cross-sectional area, A at any point in space.

RESISTANCE AND RESISTIVITY

The electrical resistance, R is defined to be the ratio of the potential difference (or voltage),   across the conductor to the current, I

The SI unit for the electrical resistance is Ohm’s Law, 

A large current flows through a conductor with small resistance

A small current flows through a conductor with a large resistance

Resistance depends on size and shape. For example,

a)      A long wire has higher resistance than a shorter wire

   b)      A thick wire to have a lower resistance than a thin wire

Figure 3: Resistance depends on size and shape

The resistance of a conductor of length, L and cross-sectional area, A can be written as

is the constant of porpotionality or resistivity of a material

Resistivity also depend on temperature. As the temperature raised, The sensitivity increases. For many materials, the relation between resistivity and temperature is linear,

 = The resistivity at temperature, 

= The resistivity at temperature, 

  = The temperature coefficient of resistivity

The SI unit is  or 

Figure 4: Resistivity and Temperature Coefficient 

A resistor is a circuit element designed to have a known resistance. In circuit analysis, it is customary to write the relationship between voltage and current for a resistor as 

Figure 5: Resistor

Resistor could be found in electronic devices.

The resistor, r called the internal resistance of the battery. When the current through a source of emf is zero, the terminal voltage (the potential difference between its terminals) is equal to emf. When the source supplies current to a load, its terminal voltage is less than the emf. There is voltage drop due to the internal resistance of the source. If the current is I and the internal resistance is r, the voltage drop across the internal resistance is Ir and the terminal voltage,

When the current is small enough, the voltage drop Ir due to the internal resistance is too small compared to ξ, hence the emf is ideal.