Significant Figures and Rounding

Rules for Significant Figures

• All digits are significant except zeros preceding a decimal fraction (e.g., 0.0045) and zeros at the end of a number containing no decimal point (e.g., 45,000).
• Non-zero digits are always significant.
• Zeros between significant figures are always significant.
• Final zeros to the right of a decimal are significant.
• Zeros are significant if they are between significant digits or are the very final thing at the end of a decimal.

Calculations and Rounding

• When adding or subtracting, round the result to the least number of decimal places present in the factors.
• When multiplying or dividing, round the result to the least number of significant figures present in the factors.
• Scientific notation expresses very large or very small numbers using a number between 1 and 10, multiplied by 10 to an exponent.
• Exponents are determined by the number of decimal places needed to move to get only one number in front of the decimal.

Electric Charges

• Electric charge causes particles to experience a force ("push" or "pull"), fundamental to electromagnetism.
• There are two types of electric charges: positive and negative.
• Positive charges are carried by protons (p+), and negative charges are carried by electrons (e-).
• Q is the symbol for charge and is used in equations such as in Coulomb's Law and Ohm's Law, to represent the amount of electric charge.
• The unit for charge is the Coulomb (C).
• One Coulomb is the charge transported by a current of one ampere in one second.
• Like charges repel and unlike charges attract due to electric field interactions.
• "The closer the charges, the greater the force between them," according to Coulomb's Law.
• Coulomb's Law mathematically states that the force (F) between two point charges (q₁ and q₂) is directly proportional to the product of the charges and inversely proportional to the square of the distance (r) between them: F = k(q1q2) / r², where k is Coulomb's constant (8.99 × 10^9 N·m²/C²).

Origin of Electrical Charge

• Atoms consist of a nucleus (protons and neutrons) surrounded by electrons in orbitals.
• Protons have a charge of +1e, electrons have a charge of -1e, and neutrons have no charge.
• Atoms have equal numbers of e- and p+, so a material has no net charge and objects remain electrically neutral under normal conditions.
• Electrons may be transferred from one material to another, creating more (-) charge on one and less (+) charge on the other.
• This process, known as charging by friction, contact, or induction, is responsible for static electricity.
• Materials with more or fewer electrons are considered "charged," with negatively charged objects having an excess of electrons and positively charged objects having lost electrons.

Coulomb's Law

• Coulomb's Law is used to calculate the force between two electric charges: F=k(q1xq2)/r^2
• F represents the electrostatic force between two charges in Newtons (N).
• k is Coulomb's constant (9 x 10⁹ Nm² C⁻² to 1 s.f OR 8.99 x 10⁹ Nm² C⁻² to 3 s.f).
• q1, q2 are the magnitudes of the two electric charges, measured in Coulombs (C).
• r is the distance between the charges, measured in meters (m).

Current

• Current is the rate of flow of charge (Q), indicating how fast electric charge moves through a circuit.
• 1 amp is equivalent to 1 Coulomb per second (1A = 1 C/s OR 1 C s⁻¹).
• Current is measured in amperes (A) or "amps," and its symbol is the letter "I."
• I = Q / t, relating current to charge and time.
• If charge flows at 1 C/s, the current is 1A; if charge flows at 2 C/s, the current is 2A; current increases proportionally with charge flow.

Measuring Current

• Current (I) is measured with an ammeter and placed in a circuit in series.
• Placing an ammeter in parallel would cause a short-circuit due to its low resistance.

Circuit Conditions

• A complete and connected circuit with a source of energy is needed for current to flow.
• If the circuit is broken, charge cannot flow, and current stops.

Current in Series Circuits

• Current is the same at any spot within the circuit.
• The rate of flow of charge doesn't change.

Current in Parallel Circuits

• Current splits at junctions and recombines later.
• The rate of flow of charge changes at different points.
• Each branch receives a portion of the total current, depending on resistance.

Conventional vs. Electron Flow

• Conventional current flows from positive to negative, as per historical convention.
• Electron flow is opposite—electrons move from negative to positive and are attracted to the positive terminal since they are negatively charged.

Voltage

• Voltage is also known as potential difference.
• The word "potential” refers to “potential” or “stored" energy (e.g., chemical energy in a battery).
• The word "difference” refers to a difference in stored energy, typically representing a "loss" as electric energy is transferred.
• It acts as electric → light energy in a bulb ; electric → sound energy in a speaker ; electric → heat energy in a resistor or heating element.
• Connection between voltage, energy, and charge: If a battery has a potential difference of 1 Volt, it gives 1 Joule of energy to each Coulomb of charge (1 V = 1 J C⁻¹).

Voltage Properties

• High voltage indicates that electrons or ions (charged material) carry a lot of energy, which allows more energy to be transferred per unit charge and can result in more powerful electrical devices.
• Voltage is measured using a voltmeter, with the symbol and unit symbol V.
• Voltmeters are connected in parallel to measure potential difference across components without interfering with the circuit current.

Electromotive Force (EMF)

• EMF stands for Electromotive Force.
• EMF is the potential difference (voltage) across a battery, power supply, or other power-providing device.
• EMF is the "force" that motivates electrons to move in a circuit, though it is a measure of energy per charge, measured in volts (V).
• EMF represents the maximum potential energy per unit charge a power source can provide before any internal losses are considered.

Circuits

• A circuit is a complete path through which electricity flows, including a power source, wires, and components like bulbs or motors.
• The parts of a circuit are: a power source (e.g., battery, power supply); conductors or wires to carry electric current; a load or device that uses electricity (e.g., light bulb, fan); and a switch to control whether the circuit is open (off) or closed (on).
• Series Circuit: components are connected in a single path, the same current flows through all components and if one component breaks, the whole circuit stops working.
• Parallel Circuits: components are connected in separate branches, current splits and flows through each branch, and if one component breaks, others still work.

Current and Charge Formula

• Current (I) is the flow of electric charge, measured in amperes (A).
• Charge (Q) is the amount of electricity measured in coulombs (C)
• I=Qt
• For example, when 6 C of charge flows in 2 seconds, the current is 3 A.

Measuring Current and Voltage

• An ammeter measures current and is placed in series.
• A voltmeter measures voltage and is placed in parallel.

Conventional vs. Electron Flow

• Conventional current flows from positive (+) to negative (-).
• Electron flow is opposite and flows from negative to positive.

Circuit Safety

• Fuses and circuit breakers protect circuits from excessive current.
• Short circuits occur when current bypasses a load, which causes overheating.

Describing Resistance

• Resistance is the opposition to the flow of electric current in a circuit.
• It results from collisions between electrons and atoms within a conductor, which slows down the movement of charge.
• The symbol for resistance is “R," and its unit is the Ohm (Ω).
• George Ohm discovered that current (I) is proportional to voltage (V), only if physical conditions (such as temperature) remain constant.
• In metal wires, increasing temperature can increase resistance due to greater atomic vibrations.

Ohm's Law

• This principle is known as Ohm's Law, represented mathematically as: I∝ V (current is proportional to voltage)
• R = V ÷ I (Resistance is voltage divided by current).
• V = IR
• I = V/R
• The relationship between voltage and current is visualized using a voltage-current graph, where a straight-line graph through the origin indicates Ohmic behavior or constant resistance.

Factors Affecting Resistance

Length of Conductor

• Longer wires have higher resistance because electrons encounter more collisions along the path.

Cross-Sectional Area (CSA)

• Wider wires have lower resistance because they provide more space for electrons to flow.

Material of the Conductor

• Materials like copper and silver have low resistance due to their high conductivity.
• Materials like rubber and glass are insulators with very high resistance.

Temperature

• Higher temperatures generally increase resistance in conductors because atoms vibrate more, leading to more frequent electron collisions.
• In some materials like superconductors, resistance drops to zero below a critical temperature.

Resistance in Series Circuits

• The total resistance in a series circuit is the sum of individual resistances: R_total = R₁ + R₂ + R₃ +
• Since current remains the same in all components, adding more resistors increases total resistance and reduces overall current flow.

Resistance in Parallel Circuits

• The total resistance in a parallel circuit is not equal to the sum of the resistors.
• It follows the formula: 1/R_total = 1 / R₁ + 1 / R₂ + 1 / R₃
• The total resistance in a parallel circuit is always less than the smallest individual resistor because multiple paths allow more current to flow.
• As more resistors are added in parallel, total resistance decreases, increasing the total current in the circuit.

Resistivity & Resistance Factors

• Resistance (R) depends on length (L), cross-sectional area (A), and the material's resistivity (ρ).
• The material itself is an intrinsic property that determines how much it resists electric current.

Understanding Resistivity

• Resistivity is a material property determining how much it opposes the flow of electricity, depending on the number of free electrons available to carry charge, and is measured in Ohm meters (Ωm) and is represented by the Greek letter Rho (ρ).
• Good conductors like copper have low resistivity, while insulators like rubber have very high resistivity.

Mathematical Relationship of Resistance

• Resistance (R) of a conductor is: Directly proportional to its length (L), so longer wires have higher resistance, and inversely proportional to its cross-sectional area (A), so thicker wires have lower resistance.
• The relationship between resistance, resistivity, length, and cross-sectional area is given by R=pLAR = \rho \frac{L}{A}R=pAL
• Where: R = Resistance (Ω) ; p = Resistivity (Ωm) ; L = Length (m) ; A = Cross-sectional area (m²).
• Materials with high resistivity have higher resistance for the same dimensions, while materials with low resistivity (like copper or silver) allow easier flow of current.

Energy

• Ability to do work, forms/expressions of energy like: electrical, heat/thermal, chemical, light, sound, mechanical energy- kinetic (motion) and potential (stored).

Law of Conservation of Energy

• Energy is not created or destroyed; it only transforms from one form to another.
• Input energy = useful energy output + wasted/dissipated energy.
• Power: the rate of energy used/consumed in a set amount of time.
• Power=energy (joules) / time (seconds).
• Power=joules/seconds (watts).
• Power ratings in watts, measures how many joules an object uses in one second.
• Eg- electrical blender uses 2400 watts, so it uses 2400 joules per second.

Power

• Electrical power=voltage (v) x current (i)
• Power=energy/time
• Voltage x current = energy/time
• Energy= voltage x current x time= power/time
• Power in terms of resistance= I x R x I = current x current x resistance
• As P=VI and V=IR
• So we can substitute 'IxR' for V, to derive : Used to dissipated energy
• Do not keep circuit on- the hotter it gets, the more the current is flowing through resistance, making energy get dissipated and making the device hotter.

Magnets

Magnetic Field Lines

• Field lines run from north to south and they never intersect.
• Appear Radial concentric, semi-circular
• Strongest when closer (concentration/density is maximum at the poles and minimum at the centers).
• Magnetic fields are strongest at the poles.
• Like poles (e.g: N + N or S + S) repel; opposite poles attract (e.g: N + S).
• Magnetic field lines show direction of force on the N-pole.
• Null point- point where there are no magnetic field lines in two repelling magnets (the part from which you cannot bring them together).

Magnetism Origin

• Electrons spin and orbit in an atom, clockwise and anti clockwise.
• If there are multiple electrons in an atom where half are going clockwise and the other half are going anticlockwise- they cancel each other other, making them un-magnetic.
• If there are multiple electrons in an atom where there are electrons who aren't cancelled out, they become magnetic.
• Magnetic materials are magnetic due to there being more atoms moving either clockwise or counterclockwise and not allowing for cancellation.
• Moving electrons create a current: a current can produce a magnetic field.
• Electrons (e-) create a magnetic effect as they orbit the nucleus.
• Some electrons behave like tiny magnets; when a material is magnetized, these tiny magnets align.
• Billions of aligned atomic magnets form one large magnet.
• If an electric current is ran though a wire, a weak magnetic field is produced from the wire.

Right Hand Grip Rule

• The Right-Hand Grip Rule shows the direction of a magnetic field around a wire.
• Point your thumb in the direction of the current (+ to -).
• Curl your fingers around the wire.
• Your fingers show the magnetic field's direction (circular pattern).

Solenoids

• A long wire with many coils is called a solenoid.

Electromagnet

• An electromagnet is a type of magnet where a magnetic field is produced by an electric current.
• It can be turned on and off.
• Strength of an electromagnet can be increased by increasing current, increasing the number of turns, and type of coil (can be area, length or material)