Electricity: Current and Circuits

Electricity Introduction

• Electricity is a controllable and convenient form of energy used in homes, schools, hospitals, and industries.
• This chapter discusses what constitutes electricity, its flow in circuits, factors controlling current, and the heating effect with applications.

Electric Current and Circuit

• Electric current is defined as the flow of electric charge through a conductor, similar to how water current is the flow of water in rivers.
• In a torch, cells or a battery provide the flow of charges to light the bulb when placed in the proper order.
• A switch makes a conducting link between the cell and the bulb, allowing current to flow when it's on.
• A continuous and closed path for electric current is known as an electric circuit; if the circuit is broken, current stops flowing.
• Electric current is quantified as the amount of charge flowing through a particular area per unit time, representing the rate of flow of electric charges.
• In metallic wires, electrons constitute the flow of charges, but historically, electric current was considered the flow of positive charges.
• Conventionally, the direction of electric current is opposite to the flow of electrons, which are negatively charged.
• If a net charge Q flows across a conductor's cross-section in time t, the current I is expressed as I = Q/t.
• The SI unit of electric charge is the coulomb (C), equivalent to the charge of approximately 6 × 10^18 electrons.
• Electric current is measured in ampere (A), named after André-Marie Ampère, where 1 A equals 1 C/1 s.
• Small currents are measured in milliampere (1 mA = 10^-3 A) or microampere (1 μA = 10^-6 A).
• An ammeter measures electric current and is connected in series within a circuit.
• Electric current flows from the positive to the negative terminal of a cell, through components like a bulb and ammeter.

Electric Potential and Potential Difference

• Electric charges flow due to a difference in electric pressure, known as potential difference, along the conductor.
• A battery, made of one or more electric cells, produces this potential difference through chemical action, even with no current drawn.
• When connected, this potential difference sets charges in motion, creating an electric current.
• To sustain current in a circuit, the cell expends its stored chemical energy.
• Electric potential difference between two points is defined as the work done to move a unit charge from one point to another: Potential difference (V) = Work done (W) / Charge (Q).
• The SI unit of electric potential difference is the volt (V), named after Alessandro Volta.
• One volt is the potential difference when 1 joule of work is required to move 1 coulomb of charge. 1 volt = 1 joule / 1 coulomb or 1 V = 1 JC⁻¹.
• A voltmeter measures potential difference and is connected in parallel across the points of measurement.

Circuit Diagram

• An electric circuit includes a cell or battery, a plug key, electrical components, and connecting wires.
• Circuit diagrams use conventional symbols to represent components.
• An electric cell is represented with one longer and one shorter parallel line.
• A battery or a combination of cells is represented with multiple long and short parallel lines.
• A plug key or switch is shown as open or closed using bracket-like symbols with or without a dot.
• A wire joint is shown as a dot where wires connect.
• Wires crossing without joining are shown as one wire arching over the other.
• An electric bulb is represented by a circle with a filament inside.
• A resistor is represented by a zig-zag line.
• A variable resistor or rheostat is represented with a zig-zag line and an arrow over it.
• An ammeter is represented by a circle with an A inside.
• A voltmeter is represented by a circle with a V inside.

Ohm's Law

• Ohm's Law describes the relationship between potential difference and current in a conductor.
• For a metallic wire, the potential difference (V) across the ends is directly proportional to the current (I) flowing through it, provided the temperature remains constant.
• Mathematically, Ohm's law is V/I = constant, where the constant is the resistance (R).
• Resistance is a conductor’s property to resist the flow of charge; its SI unit is ohm (Ω).
• According to Ohm's law, R = V/I.
• If the potential difference is 1 V and the current is 1 A, the resistance is 1 Ω (1 ohm = 1 volt / 1 ampere).
• The current through a resistor is inversely proportional to its resistance, I = V/R.
• A variable resistance (rheostat) regulates current without changing the voltage source.

Factors Affecting Resistance

• Resistance depends on a material's length, cross-sectional area, and nature.
• Resistance is directly proportional to length (l) and inversely proportional to the area of cross-section (A): R ∝ l/A.
• Resistivity (ρ) is a material property in the equation R = ρ(l/A); its SI unit is Ωm.
• Metals and alloys have low resistivity (10⁻⁸ Ωm to 10⁻⁶ Ωm) and are good conductors.
• Insulators (rubber, glass) have high resistivity (10¹² to 10¹⁷ Ωm).
• Alloys' resistivity is generally higher than their constituent metals; they are used in heating devices due to their resistance to oxidation at high temperatures.
• Tungsten is used in electric bulbs, while copper and aluminum are used in transmission lines.

Resistance of a System of Resistors

• Resistors can be combined in series or parallel in electric circuits.
• In a series circuit, resistors are joined end to end, so the current is the same through each resistor.
• The total potential difference across a series combination is the sum of the potential differences across the individual resistors: V = V₁ + V₂ + V₃.
• In a series connection, the equivalent resistance R is the sum of individual resistances: R = R₁ + R₂ + R₃.
• In parallel circuits, resistors are connected together between two points, dividing the current among the branches.
• The total current equals the sum of the current through each branch: I = I₁ + I₂ + I₃.
• The reciprocal of the equivalent resistance in a parallel circuit equals the sum of the reciprocals of the individual resistances: 1/R = 1/R₁ + 1/R₂ + 1/R₃.

Heating Effect of Electric Current

• A battery or cell provides electrical energy, maintaining current flow in a circuit.
• Some source energy does useful work, while the rest is expended as heat which raises the gadget's temperature.
• In purely resistive circuits, source energy dissipates as heat i.e why there is a heating effect of electric current.
• The power input to a circuit is P = VQ/t = VI, where V is potential difference and I is current.
• The heat produced in timet with a steady current I is H = VIt, called Joule's law of heating.
• Joule’s law of heating states that the heat developed in a resistor is directly related to the square of current for a given resistance, resistance, and duration.
• In practical situations, heat is calculated using the relation Eq. (11.21) or after the current with using the relation i.e. I = V/R

Practical Applications of Heating Effect of Electric Current

• Heat is inevitably generated in conductors when an electric current is active
• Though this can be undesirable,it also has practical uses.
• Some useful appliances are electric laundry irons, electric toasters, electric ovens, electric kettles and electric heaters.
• Electric bulbs use electric heating to produce light, requiring filaments that retain heat and withstand high temperatures (such as tungsten, which has a melting point of 3380°C).
• Bulbs are filled with chemically inactive nitrogen and argon gases.
• Another use is the fuse used in circuits which protects by stopping high electric current

Electric Power

• Definition: The rate of doing work, equal to the rate of energy consumption.
• Equation & Units: P = VI; the SI unit of power is watt (W).
• 1 W = 1 volt × 1 ampere = 1 VA.
• Commercial Unit: Kilowatt hour (kWh) known as the 'unit'.
• 1 kWh = 3.6 × 10^6 joule (J).