Current Electricity Concept Page - 3

Example

Examples of conductors

Conductors have electrons which are free to move. These electrons are the outer shell electrons of an atom. They are not so tightly bound to the nucleus. Such electrons are present in metals such as silver, copper, gold.
Hence most of the metals are good conductors of electricity. 

Example

Examples of insulators

Insulators are the elements which are bad conductors of electricity. 
Some of the examples are 1. Glass. 2. Plastic. 3. Rubber. 4. Porcelain. 5. Wood. 6. Distilled or pure water. 

Definition

Difference between conductors and insulators

S.No.	Conductor	Insulator
1	Substance which allows electricity to pass through them is called conductors	Substance which does not allow electric current to pass through it is called insulators.
2	Metals like copper,iron,aluminium etc are conductors.	Plastic,wood,rubber glass etc are insulators.
3	Resistance of conductors is very low.	Resistance of insulator is high.
4	Energy band gap is zero.	Energy band gap is widest of 10 eV.

Definition

Resistance

Resistance(R$R$) of a material is a measure of the obstruction offered to the flow of current through the material. It is caused due to inter-collisions of electrons. It is a function of the material, dimensions and the temperature of the resistor. For conductors, resistance increases linearly with temperature. It unit is 1 Ω(ohm)=1 VA−1$1\mathrm{\Omega }(ohm)=1{VA}^{-1}$.
R=ρlA$R={\displaystyle \frac{\rho l}{A}}$
where,
ρ:$\rho :$ Resistivity, function of the nature of material 
l:$l:$ Length of the resistor
A:$A:$ Area of the resistor 

Formula

Temperature dependence of resistance

R(T)=R(T0)[1+α(T−T0)]$R(T)=R(T_0)[1+\alpha (T-T_0)]$
Where R(T)$R(T)$ is the final resistance at temperature T$T$
R(T0)$R(T_0)$ is the initial resistance at temperature T0$T_0$
and α$\alpha$ is the temperature coefficient of resistivity.

Definition

Temperature dependence of resistivity

As the temperature of a conductor increases, the thermal agitation increases and the collisions become more frequent. The average time τ$\tau$ between the successive collisions decreases and hence the drift speed decreases. Thus as the temperature increases, the conductivity decreases and the resistivity increases. 
ρ(T)=ρ(T0)[1+α(T−T0)]$\rho (T)=\rho (T_0)[1+\alpha (T-T_0)]$
where ρ(T)$\rho (T)$ and ρ(T0)$\rho (T_0)$ are the resistivities at temperatures T$T$ and T0$T_0$ respectively and α$\alpha$ is the temperature coefficient of resistivity

Diagram

Variation of conductivity of conductor, insulator and semiconductor with temperature

Example

Temperature of resistance heated due to electric current

Example:
A resistance R is connected across a voltage supply V. Find the time required to raise the temperature of the resistor by ΔT$\mathrm{\Delta }T$. Given specific heat capacity of the resistor is s. Assume that resistance value is approximately constant.
Solution:
Power supplied to the resistor P=V2R$P={\displaystyle \frac{V^2}{R}}$
Heat generated in time t, Q=Pt=V2Rt$Q=Pt={\displaystyle \frac{V^2}{R}}t$
Heat generated is also given by Q=msΔT$Q=ms\mathrm{\Delta }T$
From  above equations, t=msΔTRV2$t={\displaystyle \frac{ms\mathrm{\Delta }TR}{V^2}}$

Definition

Wire bound and carbon resistors

Wire bound resistor	Carbon resistor
Withstand unusually high temperatures of up to 4500${}^0$C	Very temperature sensitive
Made by winding a metal wire, usually nichrome, around a ceramic, plastic, or fiberglass core	Made of carbon clay composition covered with a plastic case
tolerance range: 0.01 % to 1 %	Tolerance range:  5% to 20 %

Definition

Colour coding of resistors

To distinguish left from right there is a gap between the C,and D bands.

• Band A is the first significant figure of component value (left side)
• Band B is the second significant figure (some precision resistors have a third significant figure, and thus five bands).
• Band C is the decimal multiplier
• Band D if present, indicates tolerance of value in percent (no band means 20%)

BookMarks

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