Current and Circuits PDF

# CURRENT AND CIRCUITS ## 11.1 POTENTIAL DIFFERENCE, CURRENT & RESISTANCE ### POTENTIAL DIFFERENCE (V) "The work done per unit charge to move a point charge from one point to the other" $V = \frac{W}{q}$ * Work done (W) * Unit = "volt"; V ### ELECTRIC CURRENT (I) * **Terms:** * **Conductor:**...

# CURRENT AND CIRCUITS ## 11.1 POTENTIAL DIFFERENCE, CURRENT & RESISTANCE ### POTENTIAL DIFFERENCE (V) "The work done per unit charge to move a point charge from one point to the other" $V = \frac{W}{q}$ * Work done (W) * Unit = "volt"; V ### ELECTRIC CURRENT (I) * **Terms:** * **Conductor:** Materials with many free electrons per unit volume * **Insulator:** Materials with very small number of free electrons per unit volume * To transfer charge... e needs to move in the same direction: direct current; D.C. * "The rate of flow of charge through the cross-sectional area of a conductor" * Unit = "ampere"; A * Flow of one coulomb of charge per second = 1 C/s ### ELECTRIC RESISTANCE (R) * "The potential difference across its ends divided by the current through it" * $R = \frac{V}{I}$ * Unit = "ohm"; Ω * = volt per ampere * The size of current depends on neither resistance * **Ohm's Law:** * "At a constant temperature, the current through the conductor is proportional to the potential difference across it" * I α V * Obeyed at small currents, constant resistance at constant temperature * The current increases as: * Resistance increases * Ohm's law not obeyed. * "Non-Ohmic device" * Other components with variable resistance: * **Light dependent resistors (LDR)** * Resistance ↑ as light intensity ↑ * **Thermistors** * Resistance ↓ as temperature ↑ * **Factors affecting resistance:** * Nature of the material * Length of the conductor * The cross sectional area of the conductor * $R = \rho \frac{l}{A}$ * Constant p = "resistivity" Ωm * ρ depends on the material of the conductor * Most metallic conductors: ↑ temperature ↑ resistance ## 11.2 VOLTAGE, POWER & EMF ### VOLTAGE "The potential difference across a conductor" * $V = IR$ ### ELECTRIC POWER "The energy per unit time dissipated in a conductor" or "the rate of doing work" * $P = \frac{work done}{time}$ * $P = \frac{qV}{t}$ * $P = IV$ * Rewriting the formula with $V = IR$ * $P = I²R$ * $P = \frac{V²}{R}$ * If we change the voltage, power will change ### ELECTROMOTIVE FORCE (EMF) (E) "The work done per unit charge in moving charge from one terminal of the battery to the other." * Unit = "volt"; V * $E = emf = \frac{W}{q}$ ### Cells & EMF * The simplest source of p.d. * p.d. created by chemical reactions in the cell creates "internal resistance" * Direction electron flow: - to + * Direction of conventional current: + to - * In general, work done is always non-electrical * $W = qE$ ## 11.3 RESISTORS IN ELECTRIC CIRCUITS ### Components (Symbols) | Component | Symbol | | - | - | | Connecting wire | - | | Cell | - | | Battery of cells | - | | Resistor | - | | D.C. Power supply | - | | A.C. Power supply | - | | Junction of conductors | - | | Crossing conductors | - | | Lamp | - | | Voltmeter | - | | Ammeter | - | | Switch | - | | Galvanometer | - | | Potentiometer | - | | Variable resistor | - | | Heating element | - | | Light dependent resistor (LDR) | - | | Thermistor | - | ### Resistors * **In series:** No junctions * V=IR, and V2=IR2, so I(R1+R2)=12V * I(2) + 1(4) = $12V$ * $6I = 12$ * $I = \frac{12V}{R_1+R_2}$ * $I = 2A$ * I = the sum of voltages: I * R_T * I = R₁ + R₂ + R₃ + ... * Current same throughout circuit * **In parallel:** * Let V be the common p.d. across the circuit * V = I₁R₁ = I₂R₂ = I₃R₃ * I = I₁ + I₂ + I₃ * I.R_T = I₁R₁ + I₂R₂ + I₃R₃ * $I=\frac{V}{R_T}$ * $I= V(\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3})$ * $\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$ * I = I₁ = I₂ = I₃, * R_T in parallel < R₁, R₂, R₃ * Current increases * **In series and parallel:** Combine the two. ## 11.4 TERMINAL POTENTIAL DIFFERENCE AND THE POTENTIAL DIVIDER ### AMMETER & VOLTMETERS * Ideal ammeter = zero resistance * Ideal voltmeter = infinite resistance ### TERMINAL POTENTIAL DIFFERENCE * Terminal p.d. = emf when there is no current in the circuit * It is less than the emf when there is current * Internal resistance = "resistance in series to the cell due to chemicals in the cell" * $V = E - Ir$ * $E = I (R + r)$ ### POTENTIAL DIVIDER * Made of two or more resistors that allows us to tap off any voltage we want that is less than the battery voltage.