Direct Current

 CURRENT

Definitions:$\\$

• The flow of charge in a definite direction per second is called electric current.$\\$

• I=$\frac{q}{t}$=$\frac{ne}{t} \\$

• If I=1A,t=1 sec then,$\\$

• Number of electrons (n)=6.25×$10^18$ electron flowing in 1 A current per second$\\$

• current is a scalar Quantity.$\\$

Drift Velocity$\\$Drift velocity is defined as the average velocity with which free electrons get drifted towards the + ve end of the conductor under the influence of an external electric field.$\\$$\vec{V_d}$ =-$\frac{e\vec{E}}{m}$ τ$\\$τ → time of Relaxation.$\\$

|$\vec{V_d}$|= $10^{-4}$m/s, τ = $10^{-14}$ second.

Relaxation Time$\\$→ It is the average time that has elapsed since each electrons suffered its last collision with the ion or atom of the conductor, while drifting forwards the + ve end of the conductor under the effect of electric field applied.$\\$

mathematically,$\\$τ= $\frac{mean free path(λ)}{r⋅m⋅s velocity of electrons (v_{rms})} \\$Note:$\\$(1) τ∝$\frac{a}{temperature}$$\\$(ii) τ ∝ $\frac{1}{R} \\$

Current Density$\\$→ current density at a point inside the conductor is the amount of current flowing per unit area around that point of the conductor, provided the area is held in a direction normal to the current.$\\$

Current Density(J) = $\frac{I}{A} \\$SI unit of current density is A/$m^2 \\$It is a vector quantity. Its direction is that of the flow of +ve charge at the given point inside the conductor.$\\$I= JAcosθ$\\$=$\vec{J}.\vec{A} \\$$\vec{A}$ is the area vector of the plane.

Resistance

Basic Info$\\$Resistance is the obstruction possessed by the conductor to the flow of current through it.$\\$R∝ρ$\frac{l}{A} \\$ρ→ resistivity$\\$l → Length of conductor$\\$A→ Cross section Area of conductor$\\$And,$\\$ρ=$\frac{m}{ne^2τ} \\$P.S.

• Resistance depends upon: temperature, nature & dimension of material.$\\$

but,$\\$

• Resistivity depends only upon temperature and nature of material.$\\$

Ohm's Law$\\$It states that,"if the physical conditions such as temperature, nature and dimensions of conductor remains constant, the current between two points in a conductor is directly proportional to the potential difference between these two points.$\\$i.e,$\\$I ∝ R$\\$I=$\frac{1}{R}$V$\\$∴ V=IR$\\$In following graph I vs V, a straight line passing through origin is observed:$\\$

Note:$\\$

• A conductor which obeys ohm's law are called ohmic conductor.$\\$

E.g:- metals, alloys$\\$

• Conductors which do not obey ohm's law are called non-ohmic conductors.$\\$

E.g:- diode valve, neon gas , junction diode, carbon compounds etc.$\\$→ I vs V graph is parabola for Zener diode.$\\$

Resistance and Temperature:$\\$$R_t=R_o(1+α∆θ) \\$$R_o$ → resistance of the conductor at $0^o$C$\\$α→ temperature co-efficient$\\$∆θ→change in temperature$\\$∆θ=t-0= $t^oC \\$$R_t$→ resistance at $t^oC \\$

• For metals, α is positive.$\\$
• For semi-conductor and insulator, α is negative.$\\$
• Alloy's (eg:-maganin, eureka, constantan etc), have less value of α$\\$
• α= 0 for super conductors.$\\$

We can say, Resistance of super conductor is also 0.

Combination of Resistor

Series Combination$\\$

Key Points:$\\$a. $R_s$= $R_1 + R_2 + R_3 \\$b. Current through each resistor is same [Resistance]$\\$c. $R_s$ > $R_1 , R_2 , R_3$ (always)$\\$d. V across $R_1 , R_2 , R_3$ is different.$\\$e. $V_s$= $V_1 + V_2 + V_3 \\$f. $V_1 : V_2 : V_3$...... = $R_1 : R_2 : R_3$........$\\$g. Used in resistance box and decorative bulbs.$\\$

Parallel Combination$\\$

Key Points:$\\$a. $\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}+ \frac{1}{R_{3}}$ b. I = $I_1 + I_2 + I_3$