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: $R ext{ is proportional to } rac{l}{A}$

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

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: $ext{σ} = rac{1}{<br>ho} = rac{l}{R ext{Area}}$

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:

  • $R<em>s = R₁ + R₂ + R₃ +…+R</em>n$

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.