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Physics – Electricity and Magnetism

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    Study Guide Physics – Electricity and Magnetism 1. Capacitors What is a Capacitor? A capacitor is an electrical device used to store electric charge . It is made of two or more conducting plates separated by an insulating material called an insulator or dielectric . When connected to a circuit, a capacitor can store energy and then release it when needed . This makes capacitors very useful in electronic devices. 1. Capacitance The ability of a capacitor to store charge is called capacitance . Capacitance is defined as the ratio of the charge stored (Q) on the plates to the potential difference (V) between them: [C = Q / V] Unit of Capacitance • Capacitance is measured in farads (F) • (1 coulomb / volt) 2. Parallel Plate Capacitor In the simplest type of capacitor, there are two parallel plates : • One plate is positively charged • The other plate is negatively charged • The plates are separated by a distance (d) For a parallel plate capacitor in a vacuum , the capacitance is:

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    Study Guide Where: • (A) = area of each plate • (d) = distance between the plates • ( \ varepsilon_0) = permittivity of free space This formula is valid only when there is a vacuum between the plates. 3. Effect of a Dielectric When a non - conducting material (dielectric) is placed between the plates: • More charge can be stored • The capacitance increases The factor by which capacitance increases is called the dielectric constant . With a dielectric filling the space between the plates, the capacitance becomes: Values of dielectric constants are listed in material property tables . 4. Energy Stored in a Capacitor A charged capacitor stores electrical energy . The energy can be calculated using any one of the following equivalent formulas: Each formula is useful depending on which quantities are known.

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    Study Guide 5. Capacitors in Parallel Capacitors are connected in parallel when: • All positive plates are connected together • All negative plates are connected together Key Points for Parallel Capacitors • The voltage across each capacitor is the same • The total charge is the sum of individual charges [Q = Q 1 + Q 2 ] Since (Q = CV): Cancel l ing (V): Rule for Parallel Capacitors The equivalent capacitance is the sum of the individual capacitances .

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    Study Guide 6. Capacitors in Series Capacitors are connected in series when: • The positive plate of one capacitor is connected to the negative plate of the next Key Points for Series Capacitors • All capacitors carry the same charge (Q) • The total voltage is shared among the capacitors In series combinations, all the capacitors have the same charge. The potential differences across the capacitors add to equal the potential difference between the terminals of the battery; therefore, Substituting these equations into the equation for potential difference gives

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    Study Guide Cancel l ing the charge gives the following expression for the equivalent capacitance for series combinations: Rule for Series Capacitors Add the reciprocals of the capacitances, then take the reciprocal of the final answer . 2. Current and Resistance Electric circuits are everywhere around us — from mobile chargers to light bulbs at home. To understand how these circuits work, we need to learn a few key ideas: current , voltage (emf) , resistance , and power . Let’s explore each one step by step. 1. Current Electric current tells us how fast electric charge is flowing through a circuit. What is current? Current (symbol I ) is defined as the amount of electric charge passing through a cross - section of a wire per unit time . In simple terms: • More charge flowing each second → larger current • Less charge flowing → smaller current Unit of current • Current is measured in amperes (A)

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    Study Guide • 1 ampere = 1 coulomb per second This definition works for: • Charges moving in metal wires • Ions moving in liquids (electrolytic cells) • Charges moving in gases 2. How fast do electrons actually move? It is tempting to imagine electrons racing around a circuit at high speed. In reality, individual electrons move very slowly . • The average speed of electrons is called the drift velocity • In a copper wire, this speed is about 10 ⁻ ⁴ m/s The drift velocity depends on: • The charge of an electron ( q ) • The cross - sectional area of the wire ( A ) • The number of free electrons per cubic meter ( n ) At this slow speed, an electron would take about 11 minutes to travel just 10 cm ! Then why does the bulb light up instantly? When the circuit is completed: • An electric field is set up throughout the wire almost immediately • Charges everywhere in the wire start moving at nearly the same time • So the bulb glows right away, even though each electron moves slowly 3. Voltage, Circuits, and Current Direction A battery provides a voltage (V) between its terminals. This voltage creates an electric field in the wire, which causes charges to move.

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    Study Guide What is a circuit? A circuit is a complete, closed conducting path that allows current to flow from one terminal of the battery to the other. Direction of current • By convention, current is defined as the direction positive charges would move • In metals, the actual moving charges are electrons (negative charges) • Therefore, electrons move opposite to the direction of current Important note: Electric fields do not exist in conductors with stationary charges, but they do exist when charges are moving , allowing current to flow. 4. Electromotive Force (emf) The electromotive force (emf) is the potential difference between the battery terminals when no current is flowing . • It is measured in volts (V) • Despite the name, emf is not a force • The term is historical, but it is still commonly used in physics 5. Resistance and Resistivity Ohm’s Law Experiments show that, for many conductors, current is directly proportional to voltage . This relationship is known as Ohm’s Law : V = IR

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    Study Guide Where: • V = voltage • I = current • R = resistance Unit of resistance • Resistance is measured in ohms (Ω) • 1 ohm = 1 volt / 1 ampere What affects resistance? The resistance of a wire depends on: 1. Length (l) – longer wires have more resistance 2. Cross - sectional area (A) – thicker wires have less resistance 3. Material – different materials resist current differently This material property is called resistivity (ρ) . • Resistivity values are found in material property tables • The unit of resistivity is ohm - meter (Ωm) The relationship between resistance and resistivity is: R = ρl/A Important distinction • A resistor is a device made specifically to resist current • Resistance can come from anything that opposes current, such as: ○ Light bulbs ○ Heating elements

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    Study Guide 6. Electrical Power and Energy Where to paste the image Figure 1 shows a simple electric circuit: • A battery supplies voltage (symbol ε ) • Wires connect the battery to a light bulb • The filament of the bulb acts as a resistor (R) Assume: • The wires have negligible resistance • The bulb is the only significant resistance in the circuit If the battery provides 6 volts : • Charges move from higher potential to lower potential • As current flows through the bulb, electrical energy is converted into light and heat Electrical power Power is the rate at which electrical energy is used or converted. Power can be calculated using any of these equivalent formulas: • P = IV

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    Study Guide • P = V² / R • P = I²R Unit of power • Power is measured in watts (W) • 1 watt = 1 joule per second = 1 ampere - volt 3. Direct Current Circuits In everyday devices like flashlights and simple lamps, electric current flows in one direction only . This type of current is called direct current (DC) and is supplied by batteries. In this section, we study two main kinds of DC circuits: 1. Circuits made using combinations of resistors 2. Circuits that contain multiple batteries and more than one loop To simplify the analysis, we assume that the connecting wires have negligible resistance . 1. Series and Parallel Resistors Every electrical component offers some resistance to the flow of current. This resistance may come from: • Light bulbs • Heating elements • Special components called resistors , designed only to oppose current 2. Resistors Connected in Series

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