1. 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.\\

  2. 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.

  3. 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} \\

  4. 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.


  1. 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.\\


    • Resistivity depends only upon temperature and nature of material.\\
  2. 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:\\

  3. 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.\\

  4. Resistance and Temperature:\\R_t=R_o(1+α∆θ) \\R_o → resistance of the conductor at 0^oC\\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

  1. Series Combination\\

  2. Key Points:\\a. R_sR_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_sV_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.\\

  3. Parallel Combination\\

  4. 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