Current Electricity

Charge and Charge Properties

  • Charge: A physical property of matter causing it to experience force in an electromagnetic field.

    • Types of Charge: Two main types - Positive and Negative.

    • Charging Process: Non-conducting bodies (e.g., glass and silk) get charged when rubbed together.

    • SI Unit of Charge (Q): Coulomb (C).

    • Formula: Q = ext{n} e, where

      • ext{n} = number of electrons

      • e = -1.6 imes 10^{-19} ext{C}

    • Charge Behavior in Materials:

    • In non-conductors: Charge resides at a point; no flow of electrons.

    • In conductors: Charge can move or flow due to a large number of free electrons.

Current

  • Current (I): The rate of flow of charge.

    • Formula: I = rac{Q}{t}

    • Measurement: Using an ammeter connected in series.

    • SI Unit of Current: Ampere (A).

    • Definition: 1 ext{ A} = rac{1 ext{ C}}{1 ext{s}}

Potential

  • Potential (V): The amount of work done per unit charge in bringing a test positive charge from infinity to that point.

    • SI Unit of Potential: Volt (V).

    • Formula: V = rac{W}{Q}

      • 1 ext{ Volt} = rac{1 ext{ Joule}}{1 ext{ Coulomb}}

    • Potential Difference: The work done per unit charge in moving a positive test charge between two points, measured using a voltmeter connected in parallel.

Resistance

  • Resistance (R): The obstruction offered to the flow of current by a conductor.

    • SI Unit of Resistance: Ohm (Ω).

    • Formula: R = rac{V}{I}

      • 1 ext{ Ohm} = rac{1 ext{ Volt}}{1 ext{ Amp}}

    • Dependency: Depends on the number of collisions electrons suffer with positive ions.

Ohm's Law

  • Ohm's Law: The current flowing through a conductor is directly proportional to the potential difference across it, provided temperature and physical conditions remain constant.

    • Formula: V = IR

Conductance

  • Conductance (G): The reciprocal of resistance.

    • Unit: Siemens (S) or ext{Ohm}^{-1}.

Limitations of Ohm's Law

  • Ohm's law is valid only under conditions of constant temperature.

    • Graphical Representation: Straight line in a V vs. I graph represents ohmic conductors; curves represent non-ohmic conductors.

    • Slope: The slope of the I-V graph indicates conductance.

Types of Conductors

  • Ohmic Conductors: Materials that obey Ohm's Law (e.g., all metallic conductors).

  • Non-Ohmic Conductors: Materials that do not obey Ohm's Law (e.g., LED, solar cell, diode, transistor, filament of a bulb).

Factors Affecting Resistance of a Conductor

  1. Material of Conductor: Materials with free electrons have low resistance.

  2. Length of Conductor: R ext{ is directly proportional to } l (Resistance increases with length).

  3. Thickness of Conductor: R ext{ is inversely proportional to } a (Increases with smaller cross-sectional area).

  4. Temperature of Conductor: R ext{ is directly proportional to temperature} (Higher temp leads to increased collisions).

Specific Resistance or Resistivity

  • Definition: Resistance of a wire of unit length and unit area of cross-section.

    • Unit: Ohm-metre (Ωm).

    • Formula: R ext{ is proportional to } rac{l}{A}

    • R = rac{
      ho l}{ ext{Area}} (or R = rac{
      ho l}{ ext{πr}^2}).

Factors Affecting Specific Resistance

  1. Different substances have different specific resistances, with metals having low and insulators having high resistivities.

    • Example: Silver has the least specific resistance, and polythene has the highest.

  2. Temperature impacts resistivity: increases for metals but decreases for semiconductors.

  • Independence: Does not depend on the shape and size of the conductor.

Conductivity

  • Conductivity: The reciprocal of specific resistance.

    • SI Unit: Siemens per metre (S/m).

    • Representation: ext{σ} = rac{1}{
      ho} = rac{l}{R ext{Area}}

Choice of Material of Wire

  • The choice depends on the intended use:

    1. Copper: For electrical connections and power transmission due to negligible resistance.

    2. Resistance wires: Made of nichrome, manganin, constantan, etc.

    3. Fuse Wire: Alloy of lead and tin (high resistivity, low melting point).

    4. Tungsten Wire: Used in electric bulb filaments (high melting point, high resistivity).

    5. Nichrome Wire: Used in heating elements (high resistivity and heating increase with temperature).

Superconductors

  • Definition: Substances that exhibit zero resistance at very low temperatures.

    • Examples: Mercury below 4.2 K, Lead below 7.25 K.

    • Usage: Limited due to challenges in achieving very low temperatures.

Electric Cell

  • Definition: A device that maintains a constant potential difference between terminals via chemical reactions, providing regular flow of charge.

    • Chemical Energy converts to Electrical Energy.

Electro Motive Force (e.m.f) of a Cell

  • Defined as the potential difference when no current is drawn from the cell; measured by voltmeter.

    • Values: Emf of Voltaic Cell = 1.08 V, Daniel Cell = 1.08 V.

Factors Affecting the EMF of a Cell

  • Dependent Factors:

    • Material of the electrodes.

    • Electrolyte used in the cell.

  • Independent Factors:

    • Shape and distance of electrodes.

    • Amount of electrolyte.

  • Definition: Energy spent (or work done) per unit charge in a complete circuit:

    • ext{ε} = rac{W}{q}

    • ext{ε} = I(R + r)

    • Relation to Terminal Voltage: ext{ε} = V + v

Terminal Voltage of a Cell (V)

  • The potential difference between terminals when current is drawn from the cell:

    • V = IR

Voltage Drop in a Cell (v)

  • Work done per unit charge in moving through the electrolyte:

    • v = Ir

  • Nature: Not available for use.

Internal Resistance of a Cell (r)

  • Resistance inside the cell that causes voltage drop.

  • Equation: v = Ir

    • Unit: Ohm.

Factors Affecting Internal Resistance (r)

  1. Surface Area of Electrodes: Inverse relation - increase in surface area decreases internal resistance.

  2. Distance Between Electrodes: Direct relation - greater distance increases resistance.

  3. Nature and Concentration of Electrolyte: Direct relation with concentration affecting resistance.

  4. Temperature: Direct relation - increased temperature decreases resistance.

Combination of Resistors

  • Resistors can be combined in three configurations for desired resistance:

    • (a) Series

    • (b) Parallel

    • (c) Both Series and Parallel

Resistance in Series

  • Connected end to end; same current through each:

    • Given resistances: R₁, R₂, R₃.

    • Equivalent resistance:

    • Using Ohm's Law:

      • V = IR₁ for one,

      • V = IR₂ for another,

      • V = IR₃ for the third.

    • Adding these yields: V = V₁ + V₂ + V₃ = IR₁ + IR₂ + IR₃ = I(R₁ + R₂ + R₃)

      • Hence, R_s = R₁ + R₂ + R₃

    • General case: For n resistors:

    • Rs = R₁ + R₂ + R₃ +…+Rn

Resistors in Parallel

  • Each end of a resistor connected at common points:

    • Voltage remains constant across each; total current is the sum of currents:

    • Formula: I = I₁ + I₂ + I₃

    • Using potential difference: I = rac{V}{R_p}

Electrical Energy and Electric Power

  • Electrical Energy Transformations:

    1. Heating elements: Convert electrical energy to heat.

    2. Electric bulbs: Convert electrical energy to light.

    3. Motors: Convert electrical energy to mechanical energy.

    4. Electrolysis: Convert electrical energy to chemical energy.

Measurement of Electrical Energy

  • Work Done: W = QV

    • Since Q = It, substitution gives: W = VIt

  • Ohm's Law Relation:

    • W = I²Rt.

  • Alternate form:

    • W = rac{V²t}{R}.

    • SI Unit: Joule (J).

Electrical Power

  • Definition: Rate at which electrical energy is supplied.

    • Formula:

    • P = rac{W}{t}

    • P = rac{QV}{t}

    • Simplified to:

      • P = VI

      • Applying Ohm's Law yields:

      • P = rac{V²}{R} or

      • P = I²R.

  • SI Unit of Electric Power: Watt (W).

    • Definition: Power consumed when 1 A current flows through a 1 V potential difference.

    • Larger Units:

    • Kilowatt (kW) = 1000 W

    • Megawatt (MW) = 10^6 W

    • Gigawatt (GW) = 10^9 W.

Commercial Unit of Electrical Energy

  • Electric Energy Calculation:

    • For power P Watts used for duration t seconds: W = P imes t

    • Practical units:

    • Watt-hour (Wh) or kilowatt-hour (kWh).

    • Conversions:

    • 1 ext{ Wh} = 3600 ext{ Joules}.

    • 1 ext{ kWh} = 3.6 imes 10^6 ext{ J}

    • Definition: Electrical energy consumed by a 1 kW appliance in 1 hour.

Power Rating of Common Electric Appliances

  • Appliance rating indicates power consumption at a specific voltage (e.g., 100 W - 220 V indicates 100 Watts at 220 V).

    • Can be used to calculate: (a) Resistance R = rac{V²}{P} (b) Safe current I = rac{P}{V}

      • This I is the maximum allowable current for safety.

Household Consumption of Electric Energy

  • Sold in kWh units; the calculation for energy consumed over time is given by:

    • E ( ext{kWh}) = P ( ext{kW}) imes t (h)

    • In watts: E ( ext{kWh}) = P ( ext{watts}) imes t(h)/1000

  • Calculation:

    • Energy consumed = V ( ext{volts}) imes I ( ext{amps}) imes t (h) / 1000

    • Cost of electricity = ext{Electrical energy in kWh} imes ext{cost per kWh}.

Heating Effect

  • Heating Effect of Current: The heat produced in a wire when current passes through is defined as the heating effect of current.

    • Expressed by Joule's Law: H = I²Rt (in Joules).

Joule's Law of Heating: Establishes the relationship between current, resistance, and heating effect.