Current Electricity Concept Page - 4

Definition

Resistivity

Resistivity of a material at a given temperature is defined as the resistance of a unit length and unit cross-section of the material. It has units of Ωm$\mathrm{\Omega }m$. Resistivity increases with increase in temperature for metals. It is dependent on the material of a conductor and temperature only.
ρ=RAl$\rho ={\displaystyle \frac{RA}{l}}$

Result

Factors affecting resistivity

Resistivity is affected by:

• Nature of material: Metals and alloys have low resistivity (≈10−8 Ωm$\approx {10}^{-8}\mathrm{\Omega }m$) while insulators have very high resistivity(>108 Ωm$>{10}^8\mathrm{\Omega }m$).
• Temperature:
  Metals- Increases with increase in temperature. 
  Semiconductors- Decreases with increase in temperature.
  Alloys- Doesn't change much on change in temperature.

Definition

Conductivity

Electrical conductivity is the reciprocal of electrical resistivity, and measures a material's ability to conduct an electric current.
σ=1ρ$\sigma ={\displaystyle \frac{1}{\rho }}$
where σ$\sigma$ is the conductivity, and ρ$\rho$ is the resistivity. 

Formula

Relationship between conductivity and mobility

Conductivity of a material is given by 
σ=neμ$\sigma =ne\mu$
where
μ:$\mu :$ Mobility
n:$n:$ Density of electrons
e:$e:$ Charge on electron

Definition

Equivalent form of Ohm's Law

j=σE$j=\sigma E$
where j$j$ is the current density,σ=1ρ$\sigma ={\displaystyle \frac{1}{\rho }}$ where ρ$\rho$ is the resistivity and E$E$ is the electric field.

Formula

Relation of current density with electric field

We know, according to Ohm's Law, V=iR$V=iR$, But R=ρlA$R={\displaystyle \frac{\rho l}{A}}$
Hence V=IρlA$V={\displaystyle \frac{I\rho l}{A}}$
Current per unit area (taken normal to the current), I/A$I/A$, is calledcurrent density and is denoted by j$j$.
Further, if E$E$ is the magnitude of the uniform electric field in the conductor whose length is l$l$, then the potential difference V$V$ across its ends is El$El$.
El=jl$El=jl$
the above equation can also be casted in vector form. The current density ( current through unit area normal to the current) is also directed along E⃗ $\overrightarrow{E}$ and is also a vector J$J$
Hence the above equation can be casted in vector form as 
E⃗ =σj⃗ $\overrightarrow{E}=\sigma \overrightarrow{j}$
where σ=1ρ$\sigma ={\displaystyle \frac{1}{\rho }}$ is called the conductivity. 

Definition

Electric Conductance

Electric conductance is defined as the reciprocal of resistance.
G=1R$G={\displaystyle \frac{1}{R}}$
Note:
Equivalent conductance is the sum of the conductances for conductors connected in parallel and makes calculations easier.

Definition

Superconductivity

The property by virtue of which certain materials show almost zero resistance at a very low temperature is called superconductivity.The materials which show property of superconductivity are called super conductors.Example:In case of mercury resistance drops abruptly to zero at 4.2 K.

Definition

Superconductors

A superconductor is a substance of zero resistance at a very low temperature. Examples: Mercury below 4.2 K, lead below 9.2 K, etc.
Since the resistance is almost zero, current setup in a semiconductor persists for a very long time.  

Definition

Uses of Superconductors

1.They are used in powerful electromagnets.
2. High temperature super conductors are used in microwave devices.
3. Super conductors are is used in magnetic resonance imaging(MRI).

BookMarks

Page 1  Page 2  Page 3  Page 4  Page 5  Page 6  Page 7  Page 8  Page 9  Page 10  Page 11
Page 12  Page 13  Page 14  Page 15  Page 16