Hello, and welcome to this audio lesson on Current Electricity. Today, we will explore the fundamental concepts that govern how electric charge flows through conductors. We will cover electric charge and current, potential difference and resistance, Ohm's law, combinations of resistors, and finally electrical power and energy. Let us begin.
First, let us understand electric charge. When two non-conducting bodies like glass and silk are rubbed together, electrons transfer from one body to another. The body gaining electrons becomes negatively charged, while the body losing electrons becomes positively charged. Thus, there are two kinds of charges: positive and negative. Like charges repel each other, while unlike charges attract.
The S.I. unit of charge is the coulomb, symbol C. Smaller units include the milli-coulomb, micro-coulomb, and nano-coulomb. One milli-coulomb equals 10⁻³ coulombs. One micro-coulomb equals 10⁻⁶ coulombs. And one nano-coulomb equals 10⁻⁹ coulombs.
The charge on an electron is −1.6 × 10⁻¹⁹ C. Therefore, one coulomb of charge represents a deficit or excess of approximately 6.25 × 10¹⁸ electrons.
Now, let us define electric current. Current is the rate of flow of charge through a conductor. Mathematically, current I equals charge Q divided by time t, or I = Q/t.
Current equals charge over time.
The S.I. unit of current is the ampere, symbol A, named after the French physicist André-Marie Ampère. One ampere is defined as the current when one coulomb of charge passes through a conductor in one second. Thus, one ampere equals one coulomb per second. 1 A = 1 C s⁻¹.
Smaller units include the milli-ampere and micro-ampere. One milli-ampere equals 10⁻³ amperes. One micro-ampere equals 10⁻⁶ amperes.
In metals, free electrons constitute the current. In electrolytes and ionized gases, both positive ions called cations and negative ions called anions contribute to current flow. Current is measured using an ammeter connected in series with the circuit.
Next, we examine electric potential and potential difference. The electric potential at a point is defined as the amount of work done per unit charge in bringing a positive test charge from infinity to that point. It is denoted by V and is a scalar quantity.
The S.I. unit of potential is the volt, symbol V, named after the Italian physicist Alessandro Volta. One volt equals one joule per coulomb. 1 V = 1 J C⁻¹. One volt is the potential at a point when one joule of work is done to bring one coulomb of charge from infinity to that point.
Potential difference, abbreviated as p.d., between two points is the work done per unit charge in moving a positive test charge from one point to the other. If W joules of work moves charge Q coulombs from point A to point B, then the potential difference Vₐ − Vᵦ equals W/Q, or V = W/Q.
Potential difference is measured using a voltmeter connected in parallel across the two points. The positive terminal of the voltmeter must connect to the point at higher potential.
Now we come to resistance. Resistance is the obstruction offered to the flow of current by a conductor. When current flows through a metal wire, free electrons drift toward the positive end. During this movement, electrons collide with fixed positive ions and lose kinetic energy, which heats the wire. This process creates resistance to electron flow.
The resistance depends on the number of collisions electrons suffer while moving through the conductor. Four factors affect resistance: the material of the conductor, its length, its thickness or cross-sectional area, and its temperature.
Here we state Ohm's law, one of the most fundamental principles in current electricity.
According to Ohm's law, the current flowing in a conductor is directly proportional to the potential difference applied across its ends, provided that the physical conditions and temperature of the conductor remain constant.
Mathematically, current I is proportional to potential difference V, so V/I = R, where R is the resistance. This constant is the resistance R of the conductor.
Therefore, voltage equals current times resistance. V = IR.
The S.I. unit of resistance is the ohm, symbol Ω, named after the German physicist Georg Simon Ohm. One ohm is the resistance of a conductor when one ampere of current flows through it upon applying one volt of potential difference. Thus, one ohm equals one volt per ampere. 1 Ω = 1 V/A.
Larger units include the kilo-ohm and mega-ohm. One kilo-ohm equals 10³ ohms. One mega-ohm equals 10⁶ ohms.
The reciprocal of resistance is called conductance, denoted by G.
Its unit is siemens, symbol S.
For a metallic conductor obeying Ohm's law, a graph of current versus potential difference yields a straight line passing through the origin. The slope of this I-V graph equals the reciprocal of resistance. However, Ohm's law is only valid when temperature remains constant.
Conductors that obey Ohm's law are called ohmic resistors or linear resistances. Examples include metallic conductors like copper, silver, aluminum, iron, and nichrome, as well as certain electrolytes at constant temperature. For these, the V-I graph is a straight line through the origin, and the ratio V/I remains constant regardless of the values of V or I.
Conductors that do not obey Ohm's law are called non-ohmic resistors or non-linear resistances. Examples include LEDs, solar cells, junction diodes, transistors, and the filament of a bulb. For these, the V-I graph is a curve, and the ratio V/I varies with voltage or current. The resistance at any point is found from the slope of the tangent to the curve at that point, called the dynamic resistance.
Let us examine how resistance depends on the physical dimensions of a conductor. Resistance is directly proportional to length l, and inversely proportional to cross-sectional area a, so R ∝ l/a. Combining these proportionalities, resistance equals rho times length over area, or R = ρl/a. R = ρl/a, where ρ is the specific resistance or resistivity of the material.
Specific resistance is a characteristic property of the material. It equals the resistance of a wire of unit length and unit cross-sectional area made of that material. The unit of specific resistance is ohm-metre. Ω m.
Metals have very low specific resistance, approximately 10⁻⁸ Ω m. Semiconductors like germanium and silicon have intermediate values around 10⁻⁵ Ω m. Insulators have extremely high specific resistance, around 10¹³ Ω m or more.
The reciprocal of specific resistance is conductivity, denoted by σ. Its unit is siemens per metre. S m⁻¹.
Superconductors are remarkable materials whose resistance drops to nearly zero at very low temperatures near absolute zero. Once current starts flowing in a superconductor, it persists indefinitely without any applied potential difference. Mercury below 4.2 K, lead below 7.25 K, and niobium below 9.2 K exhibit superconductivity.
Now we turn to the electromotive force of a cell. A cell converts chemical energy into electrical energy through chemical reactions between its electrodes and electrolyte. The electromotive force, or e.m.f., denoted by ε, is the energy spent per unit charge in moving a positive test charge around the complete circuit of the cell, both inside and outside. Its unit is the volt.
When no current is drawn, the potential difference between the cell's terminals equals its e.m.f. However, when current flows, the terminal voltage becomes less than the e.m.f. due to energy loss within the cell. This energy loss per unit charge is called the voltage drop inside the cell.
The relationship is: terminal voltage equals e.m.f. minus voltage drop. V = ε − v.
The resistance offered by the electrolyte inside the cell is called internal resistance, denoted by r. When current I flows, the voltage drop equals current times internal resistance. v = Ir. Therefore, terminal voltage equals e.m.f. minus current times internal resistance. V = ε − Ir.
Internal resistance depends on the surface area of electrodes, the distance between electrodes, the nature and concentration of electrolyte, and the temperature of the electrolyte.
Let us now study how resistors combine in circuits. Resistors can be connected in series, in parallel, or in combinations of both.
In series combination, resistors are joined end-to-end, providing a single path for current. The same current flows through each resistor. The total potential difference equals the sum of potential differences across individual resistors. The equivalent resistance equals the sum of individual resistances. Rₛ = R₁ + R₂ + R₃, and in general Rₛ = R₁ + R₂ + ... + Rₙ.
In parallel combination, one end of each resistor connects to one point, and the other ends connect to another point. The potential difference across each resistor is the same. The total current equals the sum of currents through individual resistors. The reciprocal of equivalent resistance equals the sum of reciprocals of individual resistances. 1/Rₚ = 1/R₁ + 1/R₂ + 1/R₃, and in general 1/Rₚ = 1/R₁ + 1/R₂ + ... + 1/Rₙ.
For two resistors in parallel, this simplifies to equivalent resistance equals product over sum. Rₚ = R₁R₂/(R₁ + R₂). The equivalent resistance in parallel is always less than the smallest individual resistance.
Now we examine electrical energy and power. Electrical energy in a circuit can be expressed in multiple ways using Ohm's law. The energy equals charge times potential difference. Electrical energy W equals charge Q times potential difference V. W = QV, where W is energy in joules, Q is charge in coulombs, and V is potential difference in volts. W = VIt. Using Ohm's law, this becomes energy equals current squared times resistance times time, W = I²Rt, or voltage squared times time over resistance, W = (V²/R)t. Here I is current in amperes, R is resistance in ohms, and t is time in seconds.
The S.I. unit of electrical energy is the joule.
Electrical power is the rate of energy supply. Power P equals energy W divided by time t, giving power equals voltage times current, P = VI. P = VI. Using Ohm's law, this becomes power equals current squared times resistance, P = I²R, or voltage squared over resistance, P = V²/R. Here V is in volts, I is in amperes, and R is in ohms.
The S.I. unit of power is the watt. One watt equals one volt times one ampere, or 1 W = 1 V A. One watt is the power consumed when one ampere flows through a circuit with one volt potential difference.
Larger units include the kilowatt, megawatt, and gigawatt. One kilowatt equals one thousand watts, or 10³ watts. One megawatt equals 10⁶ watts. One gigawatt equals 10⁹ watts.
For practical purposes, electrical energy is often measured in watt-hours or kilowatt-hours. One watt-hour equals 3600 J, since one hour equals 3600 s. One kilowatt-hour, the commercial unit of electricity, equals 3.6 × 10⁶ J. Electricity bills are calculated based on kilowatt-hours consumed.
Electrical appliances are rated with power and voltage values. From these ratings, we can calculate the resistance of the appliance using resistance equals voltage squared over power, R = V²/P, and the safe current using current equals power over voltage, I = P/V. Here P is the power rating in watts, and V is the rated voltage in volts.
When current flows through a resistor, heat is produced according to Joule's law of heating. The heat produced equals current squared times resistance times time in joules, H = I²Rt joules, or 0.24 times current squared times resistance times time in calories, H = 0.24 I²Rt calories. This is Joule's law of heating, where the factor 0.24 converts joules to calories. This heating effect depends on the square of current, the resistance, and the time of current flow.
Let us now recap the key takeaways from this lesson.
First, electric current is the rate of flow of charge, measured in amperes, where one ampere equals one coulomb per second.
Second, Ohm's law states that current is directly proportional to potential difference at constant temperature, expressed as voltage equals current times resistance, where resistance is measured in ohms. V = IR, where V is in volts, I is in amperes, and R is in ohms.
Third, resistance depends on length, cross-sectional area, material through resistivity, and temperature. The formula is resistance equals resistivity times length over area. R = ρl/a, where ρ is resistivity in ohm-metres, l is length in metres, and a is area in square metres.
Fourth, in series combination, equivalent resistance equals the sum of individual resistances. In parallel combination, the reciprocal of equivalent resistance equals the sum of reciprocals of individual resistances.
Fifth, a cell's terminal voltage equals its e.m.f. minus the voltage drop across its internal resistance. V = ε − Ir, where ε is e.m.f. in volts, I is current in amperes, and r is internal resistance in ohms.
Sixth, electrical power can be calculated as power equals voltage times current, equals current squared times resistance, equals voltage squared over resistance. P = VI = I²R = V²/R, with P in watts, V in volts, I in amperes, and R in ohms.
That concludes our lesson on Current Electricity. Master these concepts and formulas, as they form the foundation for understanding electrical circuits. Practice applying Ohm's law and the resistor combination rules to various circuit problems. Keep exploring, keep learning, and see you in the next lesson.