ch 3- current electricity

Ohm’s law

At constant temperature current flowing through a circuit is directly porportional to the potential difference between its ends.

resistance

unit ohm

resistivity

conductivity

ρ=1/σ

unit- ohm meter

σ=1/ρ

unit- mho meter or ohm^-1meter

current density

Electric current flowing normally per unit area around a point

j=I/A
unit- A/m² or Am^-2

drift velocity

average velocity with which free electrons are drifted under the influence of an electric field.

v_d= -Eeτ/m_e

Relaxation time (τ)

average time interval between succesive collisions of electrons with the atom.

relation between relaxation time and drift velocity

v_d= -Eeτ/m_e

mobility (μ)

v_d/E=eτ/m_e

unit- m²s^-1V^-1
magnitude of drift verlocity per unit electric field

relation bewtween Vd and current

I=nAev_d

Ohm’s law in vector form

j=Eσ

limitation of ohm’s law

Ohm’s law is not a basic law nature. Conductors which do not follow ohm’s law as called non ohming conductors

• V ceases to be proportional to I.

• relation between V and I varies with the sign of V ex- diodes

• relation between V and I are not unique. That is for the same value of current different values of voltage are obtained. Ex- GaAs

difference between Ohmic and non-Ohmic conductors

Ohmic conductors are conductors which obey ohm’s law (graph of V and I is linear) and non ohmic conductors are conductors which do not obey ohm’s law (graph of V and I is not linear)

ex of ohmic conductors- metal, nichrome

ex of non-ohmic conductors- semiconductors, diodes and transformers

why is nichrome, magnin and constantan used as resistance coils in resistance boxes?

temp coefficient small value

resistivity is high

Magnin- Cu, Mn, Ni

Constantan- Cu, Ni

Nichrome- Ni, Cr

temp coefficient for conductors, semiconductors, alloys

resistivity vs. temp graph

metals- positive semiconductors+insulators- negative, alloys- smaller than pure metals

expression for temperature co-efficient of resistivity

ρ_T= ρ₀[1+α(T-T₀)]

ρ_T= resistivity at T^oC

ρ_o=resistivity at 0^oC

α=temperature coefficient of resistivity unit K^-1

Internal resistance r

resistance offered by the cell when current flows through it

relation connecting terminal potential difference and Emf

EMF=terminal potential difference+lost volt

V = ε – Ir

EMF (ε) vs. terminal potential difference (V)

EMF potential difference between the positive and negative electrodes of a cell in an open circuit i.e. no current flowing through the cell.

terminal potential difference is the potential difference between positive and negative electrodes of a cell in a closed loop i.e. current flows through the cell.

Kirchoff’s junction rule and loop rule

At any junction, sum of current entering the junction is equal to the sum of current leaving the junction.

Algebraic sum of change in potential around any closed loop involving resistors and cells is 0.

wheatstone bridge principle

When the bridge is balanced, I_g=0,

R₂/R₁=R₄/R₃