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Electric Current and Direct-Current Circuits Pre AP Mrs. Martin

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The Electric Battery Converts chemical energy into electrical energy Converts chemical energy into electrical energy Made of two dissimilar metals Made of two dissimilar metals One metal becomes positively charged and the other becomes negatively charged One metal becomes positively charged and the other becomes negatively charged

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The Electric Battery

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Electric Current Flow of electric charge from one place to another Flow of electric charge from one place to another Formula Formula I = Q/t I = Q/t I = Current (Ampere, A) I = Current (Ampere, A) Q = Charge (C) Q = Charge (C) t = time (s) t = time (s)

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Example Problem The disk drive in a portable CD player is connected to a battery that supplies it with a current of 0.22 A. How many electrons pass through the drive in 4.5s? The disk drive in a portable CD player is connected to a battery that supplies it with a current of 0.22 A. How many electrons pass through the drive in 4.5s?

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Direction of Current Flow When speaking of current we are referring to the direction of positive flow. When speaking of current we are referring to the direction of positive flow. Sometimes called conventional current Sometimes called conventional current

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Two types of Current Direct Current (DC) Direct Current (DC) Current always flows in one direction Current always flows in one direction Alternating Current (AC) Alternating Current (AC) Current is periodically reversed Current is periodically reversed

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Batteries and Electromotive Force Electromotive Force Electromotive Force The potential between terminals of batteries The potential between terminals of batteries Called EMF Called EMF Battery has a little internal resistance Battery has a little internal resistance Also called terminal voltage Also called terminal voltage

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Schematic Diagrams Diagram of a circuit Diagram of a circuit

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Electromotive Force Difference in electric potential between the terminals Difference in electric potential between the terminals Called emf Called emf Electron flow begins instantly, but is very slow Electron flow begins instantly, but is very slow

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Resistance and Ohms Law Resistance Resistance Opposition to the flow of electrons Opposition to the flow of electrons Like Friction for electricity Like Friction for electricity Ohms Law Ohms Law V = IR V = IR V = Potential Difference (V) V = Potential Difference (V) I = Current (A) I = Current (A) R = Resistance (Ω) R = Resistance (Ω)

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Example A potential difference of 24 V is applied to a 150 Ω resistor. How much current flows through the resistor? A potential difference of 24 V is applied to a 150 Ω resistor. How much current flows through the resistor?

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Resistivity The quality of that characterizes the resistance of a given material. The quality of that characterizes the resistance of a given material. Represented as ρ Represented as ρ The greater the resistivity, the greater the resistance The greater the resistivity, the greater the resistance

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Resistance Formula Formula R = ρ (L/A) R = ρ (L/A) R = Resistance (Ω) R = Resistance (Ω) ρ = Resistivity (Ω m) ρ = Resistivity (Ω m) L = Length of wire (m) L = Length of wire (m) A = Cross-sectional area of wire (m 2 ) A = Cross-sectional area of wire (m 2 ) Example: Example: A current of 1.82 A flows through a copper wire 1.75 m long and 1.10 mm in diameter. Find the potential difference between the ends of the wire. The resistivity of copper is 1.68 x Ωm A current of 1.82 A flows through a copper wire 1.75 m long and 1.10 mm in diameter. Find the potential difference between the ends of the wire. The resistivity of copper is 1.68 x Ωm

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Temperature Dependence and Superconductivity As electrons move, the conductor become hot As electrons move, the conductor become hot The hotter the conductor, the more resistivity due to increased Kinetic Energy The hotter the conductor, the more resistivity due to increased Kinetic Energy Superconductor Superconductor Conducts with little or no resistivity Conducts with little or no resistivity Must be at very low temperatures Must be at very low temperatures

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Electric Power Rate of change of energy Rate of change of energy P = W/t P = W/t Formula Formula P = IV P = IV P = Power (W) P = Power (W) I = Current (A) I = Current (A) V = Potential Difference (V) V = Potential Difference (V) Example Example A handheld electric fan operates on a 3.00 V battery. If the power generated by the fan is 2.24 W, what is the current supplied by the battery? A handheld electric fan operates on a 3.00 V battery. If the power generated by the fan is 2.24 W, what is the current supplied by the battery?

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Power dissipated in a resistor P = V 2 /R P = V 2 /R P = Power (W) P = Power (W) V = Potential Difference (V) V = Potential Difference (V) R = Resistance (Ω) R = Resistance (Ω) Example Example A battery with an emf of 12 V is connected to a 545 Ω resistor. How much energy is dissipated in the resistor in 65s? A battery with an emf of 12 V is connected to a 545 Ω resistor. How much energy is dissipated in the resistor in 65s?

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Energy Usage Kilowatt hours are used by electric companies to bill for energy usage. Kilowatt hours are used by electric companies to bill for energy usage. 1kWh = 3.6 x 10 6 J 1kWh = 3.6 x 10 6 J Example Example A holiday goose is cooked in the kitchen oven for 4.00 hr. Assume that the stove draws a current of 20.0 A, operates at a voltage of V, and uses electrical energy that costs $0.048 per kWh. How much does it cost to cook your goose? A holiday goose is cooked in the kitchen oven for 4.00 hr. Assume that the stove draws a current of 20.0 A, operates at a voltage of V, and uses electrical energy that costs $0.048 per kWh. How much does it cost to cook your goose?

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Household Circuits A household circuit can become overloaded if too much current flows through the circuit than is considered safe A household circuit can become overloaded if too much current flows through the circuit than is considered safe Circuit breakers and fuses are installed Circuit breakers and fuses are installed They act as switches and break the current when the current becomes too large. They act as switches and break the current when the current becomes too large.

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Resistors in Series Equivalent Resistance Equivalent Resistance Total Resistance for a circuit Total Resistance for a circuit Series Circuit Series Circuit Resistors connected one after another Resistors connected one after another All resistors have the same current All resistors have the same current Potential Difference across the resistors must sum to the emf of the battery Potential Difference across the resistors must sum to the emf of the battery R eq = R 1 + R 2 + R 3 … R eq = R 1 + R 2 + R 3 …

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Example Problem A circuit consists of three resistors connected in series to a 24.0 V battery. The current in the circuit is A. Given that R1 = Ω and R2 = Ω, find (a) the value of R3 and (b) the potential difference across each resistor. A circuit consists of three resistors connected in series to a 24.0 V battery. The current in the circuit is A. Given that R1 = Ω and R2 = Ω, find (a) the value of R3 and (b) the potential difference across each resistor.

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Resistors in Parallel Parallel Circuit Parallel Circuit Connected across the same potential difference. Connected across the same potential difference. The total current is the sum of all the individual currents The total current is the sum of all the individual currents Potential difference is the same across each resistor Potential difference is the same across each resistor 1/R eq = 1/R 1 + 1/R 2 + 1/R 3 … 1/R eq = 1/R 1 + 1/R 2 + 1/R 3 …

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Example Consider a circuit with three resistors, R1 = Ω, R2 = Ω, and R3 = Ω, connected in parallel with a 24.0 V battery. Find (a) the total current supplied by the battery and (b) the current through each resistor. Consider a circuit with three resistors, R1 = Ω, R2 = Ω, and R3 = Ω, connected in parallel with a 24.0 V battery. Find (a) the total current supplied by the battery and (b) the current through each resistor.

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Combination Circuits In the circuit shown in the diagram, the emf of the battery is 12.0 V, and all the resistors have a resistance of 200 Ω. Find the current supplied by the battery to this circuit. In the circuit shown in the diagram, the emf of the battery is 12.0 V, and all the resistors have a resistance of 200 Ω. Find the current supplied by the battery to this circuit.

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Kirchhoffs Rules The Junction Rule The Junction Rule Charge conservation Charge conservation The current entering any point in a circuit must equal the current leaving that point The current entering any point in a circuit must equal the current leaving that point The algebraic sum of the currents should equal zero The algebraic sum of the currents should equal zero + current going into the point, - current going out of the point + current going into the point, - current going out of the point

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The Loop Rule Energy Conservation Energy Conservation The algebraic sum of all potential differences around a closed loop in a circuit is zero. The algebraic sum of all potential differences around a closed loop in a circuit is zero. Example Problem Example Problem

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Capacitors in Parallel Equivalent Capacitance is the sum of all the capacitors. Equivalent Capacitance is the sum of all the capacitors. ΣC = C1 + C2 + C3 … ΣC = C1 + C2 + C3 … Example Example Two capacitors, one 12.0μF and the other of unknown capacitance are connected in parallel across a battery with an emf of 9.00 V. The total energy stored in the two capacitors is J. What is the value of the capacitance C? Two capacitors, one 12.0μF and the other of unknown capacitance are connected in parallel across a battery with an emf of 9.00 V. The total energy stored in the two capacitors is J. What is the value of the capacitance C?

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Capacitors in Series Σ1/C eq = 1/C 1 + 1/C 2 + 1/C 3 … Σ1/C eq = 1/C 1 + 1/C 2 + 1/C 3 … Example Example Consider the electrical circuit drawn, consisting of a 12 V battery and three capacitors connected partly in series and partly in parallel. Find (a) the equivalent capacitance of this circuit and (b) the total energy stored in each capacitor. Consider the electrical circuit drawn, consisting of a 12 V battery and three capacitors connected partly in series and partly in parallel. Find (a) the equivalent capacitance of this circuit and (b) the total energy stored in each capacitor.

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Ammeter Designed to measure the current in a particular part of a circuit. Designed to measure the current in a particular part of a circuit. Must be hooked up in series Must be hooked up in series

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Voltmeter Measures the potential difference across two points Measures the potential difference across two points Must be in parallel to the circuit. Must be in parallel to the circuit.

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