Current Electricity Short Notes PDF

# CURRENT ELECTRICITY ### Electric current - The rate of flow of electric charge in a definite direction through any cross-section is called electric current. - Electric current is defined as **$I = \frac{Q}{T}$**, where Q is the charge flowing through the cross-section in time T. - SI unit of ele...

# CURRENT ELECTRICITY ### Electric current - The rate of flow of electric charge in a definite direction through any cross-section is called electric current. - Electric current is defined as **$I = \frac{Q}{T}$**, where Q is the charge flowing through the cross-section in time T. - SI unit of electric current is Ampere. - **1 Ampere = 1 Coulomb / 1 second** ### Charge Carriers - **In Metals:** free electrons - **In Electrolytes:** Ions - **In Gases:** Free electrons and ions ### Electric Current as a Scalar Quantity - Electric current has a direction but it follows Algebraic addition not vector addition. - This means that the total current in a circuit is the algebraic sum of the currents in each branch of the circuit. ### Current Density - It is defined as the current flowing per unit area held normal to the flow of charge. - Current density is a vector quantity, its direction is same as the direction of flow of positive charge. - **$J = \frac{I}{A}$** - **$J = \frac{I}{ACos\theta}$** - **$I = JACos\theta$** - **$I = J.A$** ### Drift Velocity - The average velocity of free electrons with they are attracted towards the positive end of the conductor is called drift velocity. - The order of drift velocity in a conductor is **$10^{-4} m/s$**. - The order of thermal velocity is **$10^{5} m/s$**. ### Relaxation Time - The time between two successive collisions of electrons is called relaxation time. - **Temperature ↑ Relaxation Time ↓** ### Mobility - The drift velocity obtained per unit electric field is called mobility. - **$M = \frac{V_d}{E} = \frac{eτ}{m}$** - **$M = \frac{eτ}{m} = \frac{m}{sV}$** - **$M = \frac{m^2}{sV}$** - **$M = m^2s^{-1}V^{-1}$** ### Ohm's Law - According to Ohm's Law, the current flowing in a conductor is directly proportional to the potential difference applied across its ends provided that physical conditions such as temperature should remain constant. - **$V \propto I$** - **$V = RI$** - **$R = \frac{V}{I}$** ### Resistance - The obstruction offered in the path of current due to collisions between electrons and ions is called resistance. - **$R\propto l$** - **$R\propto \frac{1}{A}$** - **$R \propto \frac{1}{A}$** - **$R = \frac{ρl}{A}$** - Where ρ is a constant called **Resistivity**. - The Resistance of 1 unit volume of conductor is the resistivity or specific resistance. - **$1m\times1m^2$ = 1 unit volume** - **$ρ$ = Resistance / $l/A$ ** - Resistivity depends only on the material and temperature of substance. ### Conductance - The reciprocal of resistance is called conductance. - **$G = \frac{1}{R}$** - SI unit = ohm-1 or Siemens ### Effect of Length on Resistance - When length is doubled, Resistance is doubled - **$R\propto l$** ### Stretching a conductor - When length is doubled by stretching, resistance is four times. - **$R_{new} = n^2.R$** - **$R_{new} = n^2.R$** ### Slope of VI Graph - The slope of VI Graph gives resistance. - **Slope of VI Graph α $\frac{1}{Slope of IV graph}$** - When resistance is positive, the slope is less than 90°. - When resistance is Negative, the slope is greater than 90°. - **In which region is Resistance negative? DE.** - **In which region does Ohm's Law work? AB** ### Relation between Free Electron Density and Relaxation Time - **$I = neAv_d$** - **$I = neA(eτ/m)$** - **$I = ne^2Aετ/m$** - **$I = ne^2AετV/ml$** - **$I = mlV/ne^2Aετ$** - **$V α I$** ### Effect of Temperature on Resistance of Conductor - **$R = ml/ne^2Aετ$** - As **Temp ↑**, Kinetic Energy ↑ - **Temp ↑**, Collisions ↑ - **Temp ↑**, Relaxation Time ↓ - **Resistivity ↑**, Resistance ↑ ### Effect of Temperature on Alloys - Alloys consist of metals and metals or metals and non-metals. - **(i) Constantan** - **(ii) Manganin** - **(iii) Nichrome** - **Effect of Temperature on Resistivity of Alloys is very Less.** - It is the reason that we use alloy wire in current electricity experiment, like potentiometer, meter bridge. ### Effect of Temperature on Resistivity of Semiconductor - **Semiconductor** acts as an insulator at low temperatures and as a conductor as temperature rises. - **Low temp 0K → Act as Insulator** - **Room temp 300K → Act as Conductor** - **T α $\frac{1}{R_ρ}$** ### Effect of Temperature on Electrolytes - As **Temp ↑**, intermolecular distance ↑ - **Temp ↑**, Collision ↓ - **Temp ↑**, Resistance ↓ ### Thermal Coefficient Of Resistance - **$α = \frac{ΔR}{R_oΔT}$** - **$α = \frac{Δρ}{ρ_oΔT}$** - **$R_oΔTα= ΔR$** - **$R_oΔTα = (R-R_o)$** - **$R_o + R_oΔTα = R$** - **$R_o(1 + ΔTα) = R$** - **$ρ = ρ_o(1 + ΔTα)$** - **$K^{-1}$** - **Conductor → α = +ve** - **Alloy → α = +ve but very low** - **Semiconductor → α = -ve** - ** Electrolyte → α = -ve** ### Electromotive Force - The energy required by a charge to complete its cycle is called Electromotive force or emf of cell. - It is not a force. - The maximum potential difference between terminals of a cell in an open circuit is called emf - The direction of current outside the cell is +ve to -ve and inside the cell is -ve to +ve - **$ε = V + Ir$** - **$ε = V$** ### Electromotive Force vs Terminal Potential Difference - Electromotive force is greater than terminal potential difference. - During recharging, terminal voltage is greater than emf. - **$ε > V$, current is drawn.** - **$V > ε$, recharging.** - **$ε = V+Ir$** - **$V = ε-Ir$** ### Internal Resistance of Cell - The resistance offered by the electrolyte of the cell to the flow of ions is called internal resistance of the cell. - **Factors Affecting Internal Resistance of Cell** - **Concentration increases, Internal Resistance increases.** - **Temperature increases, Internal Resistance decreases.** - **Separation between electrodes Increases, Internal Resistance increases.** - **Internal Resistance is inversely proportional to immersed surface area of electrode.** ### Short Circuit - In the case of a short circuit, - **$R= 0$** - **$I_{max} = \frac{ε}{r}$** - **$I = \frac{ε}{R+r}$** ### Condition for Maximum and Minimum Current in Series Combinations - Let the emf and internal resistance of each cell connected in series is ε and r respectively. - **$R = $ external resistance** - **If $R <nr$**, **$I = \frac{ne}{nr}$** - **If $R>nr$**, **$I = \frac{ne}{R}$** - **$I = \frac{nε}{R+nr}$** - **$I = \frac{ε}{r}$** ### Condition for maximum and minimum current in parallel combination - For Maximum current, **$R>>mr$** - **$I = \frac{mε}{r}$** - For minimum current, **$R<<mr$** - **$I = \frac{mε}{mR}$** - **$I = \frac{ε}{r+mR/m}$** - **$I = \frac{mε}{r+mr}$** ### Kirchhoff's Rule - **Kirchhoff's current Rule (Junction Rule)** : The algebraic sum of the current at the junction is always zero - **Kirchhoff's Voltage Law (Loop Law):** Sum of all change in potential difference around the closed loop is Zero. - **ΣI = 0** - **$I_1 + I_2 + I_3 - I_4 - I_5 = 0$** - **$I_1 + I_2 + I_3 = I_4 + I_5$** - **$I_1 + I_2 + I_3 = I_4 + I_5$** - **ΣΔV = 0** - **Current reaching Junction = Current leaving Junction** - KCL follows conservation of charge. ### How to assign signs in Kirchhoff's Law - If we go through a resistor in the direction of current, then the potential drop is negative. - If we go through a resistor in the opposite direction of the current, then the potential drop is positive. ### Electric Power - **$P = \frac{W}{T}$** - **$P = \frac{(V.q)}{T}$** - **$P = VI$** - **$P = IR.I$** - **$P = I^2R$** - **$P = V.V_R$** - **$P = V^2/R$** ### Electrical Energy - **Unit of energy is Joule.** - **Commercial Unit is KWh**, which is defined as **1KWh = 3.6×10^6J**. - **1KWh = 1 Unit (Meter Reading)** - **Power = work/Time** - **Power = energy/time** - **Energy = Power×Time** - **Energy = I^2RT** - **Heating = I^2RT** ### Power Rating - The power that is marked on devices of given voltage is called rated power. - A device may deliver different power at different voltage, but its resistance will always remain constant ### Problem: find power consumed by a bulb of 100W when used at 200V. - **Given:** - **P = 100W** - **V = 220V** - **R = V^2/P = 220×220/100 = 484Ω** - **$P_{consumed} = \frac{V^2_{given}}{R} = \frac{100}{1.21} $ = 82W** ### Brightness of Bulbs - **Which bulb will glow brighter?** - **Bulb 1:** - **R = 220×220/440 = 110Ω** - **I = V/R = 220/550 = 0.4A** - **$P_{cons1} = I^2R$ = 0.16 × 110 = 17.6 W** - **Bulb 2:** - **R = 220×220/110 = 440Ω** - **I = V/R = 220/550 = 0.4A** - **$P_{cons2} = I^2R$ = 0.16 × 440 = 70.4 W** - - **In Series: Brightness α Pconsumed** - **In Series: Rated Power ↑ , Heating ↑ , Brightness ↓**