Electric Charge: Properties and Types

• Charge is a property of matter exhibiting electromagnetic effects.
• Electromagnetic effect is a property with both electricity and magnetic aspects.

Types of Charge

• Positive charge is a charge on a proton or due to electron loss; proton number exceeds electron number.
• Negative charge is a charge on an electron or due to electron gain; electron number exceeds proton number.
• Protons and electrons possess the same magnitude of charge.

Properties of Charge

• Like charges repel.
• Unlike charges attract.
• The SI unit of charge is the Coulomb (C), represented as Q or q.
• One coulomb is the charge amount exerting a force of 9 × 10^9 N on an equal charge at 1 meter distance.
• One electron has a charge of -1.6 × 10^-19 C.
• One proton has a charge of 1.6 × 10^-19 C.
• One coulomb is equivalent to the combined charge of 6.25 × 10^18 electrons.

Classification of Materials

• Conductors are substances allowing electricity to pass through.
• Insulators are substances not allowing electricity to pass through.
• Conductors and insulators are neutral; electrons in conductors move freely, while in insulators, they do not.
• Static electricity involves electric charges at rest, current electricity involves electric charges in motion.
• An electric field is a region around a charge where its influence is experienced, possessing magnitude and direction.
• Electric potential is the work done in bringing a unit positive charge from infinity to a specific point in an electric field.
• Potential difference is the work done to move a unit charge from one point to another, or the difference in electric potential between two points.
• Potential difference equals work done divided by charge (V = W/Q).
• The SI unit of potential difference is the Volt.
• Potential difference is also known as voltage.
• One volt is the potential difference between two points in a conductor when 1 joule of work moves a charge of 1 coulomb.
• Potential difference is path independent.
• A voltmeter measures potential difference, connected in parallel across points of interest.
• Voltmeter resistance is high to ensure negligible current draw.
• Electric current is the rate of electric charge flow through a conductor's cross-section.
• Potential between two points causes charge flow, producing current.
• Current equals charge divided by time (I = C/t).
• Only electrons flow in a conductor to produce current.
• The SI unit of current is the ampere.
• One ampere is one coulomb of charge flowing through a conductor's section in one second.
• 1A equals 1C per 1 sec.
• The actual direction of electric current is the motion of negative charge, conventionally, positive charge motion.
• An ammeter measures electric current, connected in series; ammeter resistance is low to avoid altering circuit current.
• An electric circuit is a closed path through which electric current flows.

Electric Symbols

• Connecting wires are represented by a straight line, and a connection or joint by a dot where lines meet.
• Wires not connected are shown with a small arc to hop over the wire in diagrams.
• A cell is represented by one long and one short parallel line, and a battery is multiple cells in series.
• An open plug or switch is represented by a broken line.
• A closed plug or switch is represented by a closed line.
• A galvanometer is represented by a circle with a "G" inside.
• Off bulbs are represented by a circle with a "X" inside it.
• An on bulb is represented by a circle with a filament inside.
• A resistor is represented by a zigzag line.
• A variable resistor or rheostat is represented by a resistor symbol with an arrow across it.
• A voltmeter is represented by a circle with a "V" inside.
• An ammeter is represented by a circle with an "A" inside.
• A fuse is represented by a line with a diagonal line through it.
• Ohm’s Law states current through a conductor is directly proportional to potential at constant temperature (I ∝ V).
• V = R × I where R is resistance.
• Resistance (R) equals V/I.
• The SI unit of resistance is the Ohm (Ω).
• One Ohm is the resistance allowing 1 ampere to flow when 1 volt is applied.
• Resistance is a conductor's property opposing electric current flow; it is a scalar quantity.
• Doubling the potential doubles the current, if all other factors are equal.

Factors Affecting Resistance

• Length: Resistance is directly proportional to length (R α l).
• Area: Resistance is inversely proportional to area (R α 1/A).
• Temperature: Resistance of metals increases with temperature.
• Material: Different materials have different resistances.
• Combining the equations yields R = ρ(l/A), with ρ as resistivity.
• Resistivity is the resistance of a substance cube with 1-meter sides.
• ρ = R if area A and length l equal 1 unit.
• The SI unit of resistivity is the Ohm meter.
• Resistivity depends on temperature and substance nature, not length or thickness.
• Metals and alloys range from 10^-8 to 10^-6 Ωm in resistivity.
• Insulators range from 10^12 to 10^17 Ωm in resistivity.
• Alloys usually have higher resistivity than their constituent metals.
• Nichrome (Nickel, Chromium, Manganese, Iron) and Manganin (Copper, Manganese, Nickel) are examples of alloys.
• Alloys resist oxidation (burning) at high temperatures, making them useful in heating devices.
• Copper and aluminum are used for electrical transmission due to low resistivity.
• A rheostat is a variable resistor regulating current without changing voltage.
• Resistors have moderate resistivity, offering resistance to current flow.
• Alloys like Nichrome, and Manganese are used for resistors.
• High-resistivity resistors serve as heating elements.
• Alloys such as Nichrome are used for this purpose due to high resistivity and oxidation resistance.
• In series, the same current flows through each resistor; the equivalent resistance can be written as R = R1 + R2 + R3 + ...

Series Combination Derivation

• If resistors R1, R2, and R3 are connected in series with current I, the potential differences are V1, V2, and V3 respectively.
• From Ohm’s law: V1 = IR1, V2 = IR2, and V3 = IR3.
• If the total potential difference is V and total resistance is R, then V = V1 + V2 + V3 and V = IR.
• Since V = V1 + V2 + V3, then IR = IR1 + IR2 + IR3 leading to IR = I(R1 + R2 + R3).

Parallel combination:

• When resistors are connected between two common points with the same potential difference, it is called a parallel combination.
• If resistors R1, R2, and R3 are connected in parallel, the equivalent resistance (R) is given by 1/R = 1/R1 + 1/R2 + 1/R3.

Parallel Combination Derivation

• If resistors R1, R2, and R3 are connected in series with potential difference V, the currents are I1, I2, and I3 respectively.
• From Ohm’s law: I1 = V/R1, I2 = V/R2, and I3 = V/R3.
• If the total current is I and total resistance is R, then I = V/R and I = I1 + I2 + I3.
• Thus, V/R = V/R1 + V/R2 + V/R3 leading to 1/R = (1/R1) + (1/R2) + (1/R3).
• The result means equivalence resistance for parallel combination is expressed as 1/R = 1/R1 + 1/R2 + 1/R3 + ...
• When a potential difference is applied across a wire, a current starts flowing. Free electrons collide with positive ions and lose energy, turning it into heat.
• Heat produced is known as the heating effect of electric current.
• Electrical energy is maintaining an electric current in an electrical circuit for a given time.
• Given V = W/Q then W = VQ or Vq.
• Apply I = Q/t then q = It
• Thus, W = V.I.t and also V = IR

Joule's Law of Heating

• Conductor-produced heat equals battery-supplied energy maintaining circuit current.
• Heat produced is proportional to the square of current, resistance, and time.
• Combining these relations, H = I^2 * R * t.
• Heat produced equals electrical energy dissipated, which can be transferred into heat.
• Then W = H = VQ or Vq
• Given I = q/t then q = It,
• Thus, W = H = VIt
• Also V = IR
• Given W = IR * I * t
• Then W = H = I^2 * R * t
• Calculate also I = V/R:
• The relations shows: W = V^2 / R * t
• W = H = V^2 / R * t
• The SI unit of electrical energy is the Joule.
• Other units are calories, and electron volts
• 1 Cal equals 4.18 J
• 1ev equals 1.6 × 10^-19 J
• Power is energy production/consumption rate.
• Electrical power is electrical energy produced/consumed per unit time.
• The basic expresssion says: P = work done per time or electrical energy per time shown as: P = W / t

Power Relations

• Previous relations yield P = I^2 * R
• Also P = V^2 / R
• Also apply expression: P = VI
• SI power unit is Watt (Joule/sec).
• One Watt is the power of appliance uses 1 ampere at 1 volt.
• Practical power unit is Horsepower: 1 hp equals 746 W.
• Commercial energy unit is Kilowatt-hour (KWH).
• 1 KWH: Energy used by 1000-watt appliance operating for 1 hour. 1 KWH is 1 unit.

KWH to Joule Conversion

• 1w = 1J/s and 1h = 60 × 60 sec = 3600 s
• 1kw = 1000 w = 1000 J/s
• 1kwh = 1kw × 1h
• 1kwh = 1000 J/s × 3600 s
• 1kwh = 3600000 J
• 1kwh = 3.6 × 10^6 J
• Number of units calculation is watt x hours /1000
• Electric irons, kettles, ovens, and heaters utilize the heating effect, often using nichrome or manganin.
• Connecting wires produce negligible heat due to low resistance.
• Light bulbs also use the heating effect; high-resistance tungsten filaments glow white-hot. Tungsten is used due to it's high melting point (3380°C).
• Bulbs contain chemically inert gases like argon and nitrogen.
• Electric fuses are safety devices protecting appliances from short circuits or overloading.
• Fuses are made of tin or copper/tin alloy, connected in series.
• High resistivity yet low metling point.

Fuse Function

• During short circuits or overloading, high resistivity and low melting point cause the fuse to break, stopping current flow, protecting appliances.