CurrentCurrent

CurrentCurrent

Current is defined as the flow of Current is defined as the flow of positive charge.positive charge.

I = Q/tI = Q/t I: current in Amperes or Amps (A)I: current in Amperes or Amps (A) Q: charge in Coulombs (C)Q: charge in Coulombs (C) t: time in seconds (s)t: time in seconds (s)

Electron FlowElectron Flow

In a normal electrical circuit, it is In a normal electrical circuit, it is the electrons that carry the charge.the electrons that carry the charge.

So if the electrons one way, which So if the electrons one way, which way does the current move?way does the current move?

ProblemProblem How many electrons per hour flow past a point in How many electrons per hour flow past a point in

a circuit if it bears 11.4 mA of direct current?a circuit if it bears 11.4 mA of direct current?

EMFEMF

Cells convert chemical energy into electrical Cells convert chemical energy into electrical energy.energy.

The potential difference (voltage) provided by The potential difference (voltage) provided by a cell is called its electromotive force (or emf).a cell is called its electromotive force (or emf).

The emf of a cell is constant, until near the The emf of a cell is constant, until near the end of the cellend of the cell’’s useful lifetime.s useful lifetime.

Misnomer: The emf is not really a force.Misnomer: The emf is not really a force.

BatteryBattery

A battery is composed of more than A battery is composed of more than one cell in series.one cell in series.

The emf of a battery is the sum of The emf of a battery is the sum of the emfthe emf’’s of the cells.s of the cells.

Circuit ComponentsCircuit Components

VoltmeterVoltmeter AmmeterAmmeter

OhmmeterOhmmeterSwitchSwitch

ProblemProblem If a typical AA cell has an emf of 1.5 V, how much If a typical AA cell has an emf of 1.5 V, how much

emf do 4 AA cells provide?emf do 4 AA cells provide? Draw the battery composed of these 4 cells.Draw the battery composed of these 4 cells.

ProblemProblem Draw a single loop circuit that contains a cell, a Draw a single loop circuit that contains a cell, a

light bulb, and a switch.light bulb, and a switch. Put a voltmeter in the circuit so it reads the Put a voltmeter in the circuit so it reads the

potential difference across the light bulb.potential difference across the light bulb.

SeriesSeries

Series components are put together Series components are put together so that all the current must go so that all the current must go through each onethrough each one

Bulbs in series all have the same Bulbs in series all have the same current.current.

ParallelParallel

Parallel components are put Parallel components are put together so that the current divides, together so that the current divides, and each component gets only a and each component gets only a fraction of it.fraction of it.

Bulbs in parallel Bulbs in parallel do notdo not have the have the same current. Their current is same current. Their current is proportional to the resistance of the proportional to the resistance of the paths.paths.

ProblemProblem Draw a circuit with a cell and two bulbs in series.Draw a circuit with a cell and two bulbs in series.

ProblemProblem Draw a circuit having a cell and four bulbs. Draw a circuit having a cell and four bulbs.

Exactly two of the bulbs must be in parallel.Exactly two of the bulbs must be in parallel.

Mini Lab AMini Lab A

Draw a circuit containing one cell, Draw a circuit containing one cell, one bulb, and a switch. Create this one bulb, and a switch. Create this with the available components. with the available components. Measure the voltage across the cell Measure the voltage across the cell and then across the bulb. What do and then across the bulb. What do you observe?you observe?

Mini Lab BMini Lab B Draw a circuit containing a cells and two Draw a circuit containing a cells and two

bulbs in series. Create this with the bulbs in series. Create this with the available components.available components.

What do you observe happens to the other What do you observe happens to the other bulb’s brightness when you unscrew one bulb’s brightness when you unscrew one of them?of them?

Measure the voltage across the battery Measure the voltage across the battery and across each bulb. What do you and across each bulb. What do you observe?observe?

Mini Lab CMini Lab C

Draw a circuit containing a cells and Draw a circuit containing a cells and two bulbs in parallel. Create this with two bulbs in parallel. Create this with the available components.the available components.

What do you observe happens to the What do you observe happens to the bulbs when you unscrew one bulb? bulbs when you unscrew one bulb?

Measure the voltage across the Measure the voltage across the battery and across each bulb. What do battery and across each bulb. What do you observe?you observe?

Mini Lab DMini Lab D

Draw a circuit containing a cells, Draw a circuit containing a cells, three bulbs in series, and a switch three bulbs in series, and a switch which shorts the last bulb when it is which shorts the last bulb when it is closed. Create this with the available closed. Create this with the available components.components.

What do you observe happens to the What do you observe happens to the bulbs when you close the switch? bulbs when you close the switch?

OhmOhm’’s Laws Law

ResistorsResistors

Resistors are devices put in circuits Resistors are devices put in circuits to reduce the current flow.to reduce the current flow.

Resistors are built to provide a Resistors are built to provide a measured amount of measured amount of ““resistanceresistance”” to to electrical flow, and thus reduce the electrical flow, and thus reduce the current.current.

Circuit ComponentsCircuit Components

ResistorResistor

ResistanceResistance

Resistance depends on resistivity Resistance depends on resistivity and on geometry of the resistor.and on geometry of the resistor.

R = R = L/AL/A : resistivity (: resistivity (ΩΩ m) m) L: length of resistor (m)L: length of resistor (m) A: cross sectional area of resistor (mA: cross sectional area of resistor (m22))

Unit of resistance: Ohms (Unit of resistance: Ohms (ΩΩ))

ProblemProblem What is the resistivity of a substance which has a What is the resistivity of a substance which has a

resistance of 1000 resistance of 1000 ΩΩ if the length of the material if the length of the material is 4.0 cm and its cross sectional area is 0.20 cmis 4.0 cm and its cross sectional area is 0.20 cm22??

iClickeriClicker

Two concentric circular loops of radii Two concentric circular loops of radii bb and and 2b2b, made of the , made of the same type of wire, lie in the plane of the page, as shown same type of wire, lie in the plane of the page, as shown above. The total resistance of the wire loop of radius above. The total resistance of the wire loop of radius bb is is RR. What is the resistance of the wire loop of radius . What is the resistance of the wire loop of radius 2b2b ? ?

(A) (A) R/4 R/4 (B) (B) R/2R/2 (C) (C) RR (D) (D) 2R2R (E) (E) 4R4R

ProblemProblem What is the resistance of a mile of copper wire if What is the resistance of a mile of copper wire if

the diameter is 5.0 mm? (resistivity of copper is the diameter is 5.0 mm? (resistivity of copper is 1.72 x 101.72 x 10-8-8))

iClickeriClicker

The five resistors shown below have the lengths The five resistors shown below have the lengths and cross‑sectional areas indicated and are made and cross‑sectional areas indicated and are made of material with the same resistivity. Which of material with the same resistivity. Which resistor has the least resistance?resistor has the least resistance?

OhmOhm’’s Laws Law

Resistance in a component in a Resistance in a component in a circuit causes potential to drop circuit causes potential to drop according to the equation:according to the equation:

ΔΔV = IRV = IR ΔΔV: potential drop (Volts)V: potential drop (Volts) I: current (Amperes)I: current (Amperes) R: resistance (Ohms)R: resistance (Ohms)

OhmmeterOhmmeter

Measures Resistance.Measures Resistance.

Placed across a resistor when no Placed across a resistor when no current is flowing.current is flowing.

AmmeterAmmeter

An ammeter measures current.An ammeter measures current.

It is placed in the circuit in a series It is placed in the circuit in a series connection.connection.

An ammeter has very low resistance, An ammeter has very low resistance, and does not contribute significantly and does not contribute significantly to the total resistance of the circuit.to the total resistance of the circuit.

PowerPower

P = W/tP = W/t

P = P = ΔΔE/E/ΔΔtt

UnitsUnits WattsWatts Joules/secondJoules/second

Power in CircuitsPower in Circuits

P = IP = IΔΔVV P: power (W)P: power (W) I: current (A)I: current (A) ΔΔV: potential difference (V)V: potential difference (V)

P = IP = I22RR

P = (P = (ΔΔV)V)22/R/R

iClickeriClicker

The product 2 amperes x 2 volts x 2 The product 2 amperes x 2 volts x 2 seconds is equal to seconds is equal to

(A) 8 coulombs (A) 8 coulombs (B) 8 newtons (B) 8 newtons (C) 8 joules (C) 8 joules (D) 8 calories (D) 8 calories (E) 8 newton‑amperes (E) 8 newton‑amperes

iClickeriClicker

The circuit shown above left is made up of a variable resistor The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance. A graph of and a battery with negligible internal resistance. A graph of the power P dissipated in the resistor as a function of the the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right. What current I supplied by the battery is given above right. What is the emf of the battery?is the emf of the battery?

(A) 0.025 V (A) 0.025 V (B) 0.67 V (B) 0.67 V (C) 2.5 V (C) 2.5 V (D) 6.25 V (D) 6.25 V (E) 40 V(E) 40 V

ProblemProblem How much current flows through a 100-W light How much current flows through a 100-W light

bulb connected to a 120 V DC power supply? bulb connected to a 120 V DC power supply? What is the resistance of the bulb?What is the resistance of the bulb?

iClickeriClicker

A certain coffeepot draws 4.0 A of current A certain coffeepot draws 4.0 A of current when it is operated on 120 V household when it is operated on 120 V household lines. If electrical energy costs 10 cents lines. If electrical energy costs 10 cents per kilowatt‑hour, how much does it cost to per kilowatt‑hour, how much does it cost to operate the coffeepot for 2 hours?operate the coffeepot for 2 hours?

(A) 2.4 cents (A) 2.4 cents (B) 4.8 cents (B) 4.8 cents (C) 8.0 cents (C) 8.0 cents (D) 9.6 cents (D) 9.6 cents (E) 16 cents(E) 16 cents

Resistors in CircuitsResistors in Circuits Resistors can be placed in circuits in a Resistors can be placed in circuits in a

variety of arrangements in order to variety of arrangements in order to control the current.control the current.

The overall resistance of a specific The overall resistance of a specific grouping of resistors is referred to as the grouping of resistors is referred to as the equivalent resistance.equivalent resistance.

The equivalent resistance in a circuit The equivalent resistance in a circuit determine the current output from the determine the current output from the battery.battery.

Resistors in CircuitsResistors in Circuits Arranging resistors in series increases the Arranging resistors in series increases the

resistance and causes the current to be resistance and causes the current to be reduced.reduced.

Arranging resistors in parallel reduces the Arranging resistors in parallel reduces the resistance and causes the current to resistance and causes the current to increase.increase.

Resistors in SeriesResistors in Series

Resistors in ParallelResistors in Parallel

iClickeriClicker

The electrical resistance of the part of the circuit The electrical resistance of the part of the circuit shown between point X and point Y is shown between point X and point Y is

(A) 4/3 (A) 4/3 (B) 2 (B) 2 (C) 2.75 (C) 2.75 (D) 4 (D) 4 (E) 6 (E) 6

iClickeriClicker

Which two arrangements of resistors shown above Which two arrangements of resistors shown above have the same resistance between the terminals?have the same resistance between the terminals?

(A) I and II (A) I and II (B) I and IV (B) I and IV (C) II and III (C) II and III (D) II and IV (D) II and IV (E) III and IV(E) III and IV

iClickeriClicker

A lamp, a voltmeter V, an ammeter A, and a battery with zero A lamp, a voltmeter V, an ammeter A, and a battery with zero internal resistance are connected as shown above. internal resistance are connected as shown above. Connecting another lamp in parallel with the first lamp as Connecting another lamp in parallel with the first lamp as shown by the dashed lines wouldshown by the dashed lines would

(A) increase the ammeter reading (A) increase the ammeter reading (B) decrease the ammeter reading (B) decrease the ammeter reading (C) increase the voltmeter reading (C) increase the voltmeter reading (D) decrease the voltmeter reading (D) decrease the voltmeter reading (E) produce no change in either meter reading(E) produce no change in either meter reading

KirchoffKirchoff’’s Ruless Rules

ProblemProblem Draw a circuit containing, in order (1) a 1.5 V Draw a circuit containing, in order (1) a 1.5 V

cell, (2) a 100-cell, (2) a 100-ΩΩ resistor, (3) a 330- resistor, (3) a 330-ΩΩ resistor in resistor in parallel with a 100-parallel with a 100-ΩΩ resistor (4) a 560- resistor (4) a 560-ΩΩ resistor, and (5) a switch.resistor, and (5) a switch.

Calculate the equivalent resistance.Calculate the equivalent resistance.

Calculate the current through the cell.Calculate the current through the cell.

Calculate the current through the 330-Calculate the current through the 330-ΩΩ resistor.resistor.

iClickeriClicker

In the diagrams above, resistors RIn the diagrams above, resistors R11 and R and R22 are shown in two are shown in two different connections to the same source of emf different connections to the same source of emf that has that has no internal resistance. How does the power dissipated by no internal resistance. How does the power dissipated by the resistors in these two cases compare?the resistors in these two cases compare?

(A) It is greater for the series connection.(A) It is greater for the series connection.(B) It is greater for the parallel connection.(B) It is greater for the parallel connection.(C) It is the same for both connections(C) It is the same for both connections(D) It is different for each connection, but one must know the (D) It is different for each connection, but one must know the

values of R1 and R2 to know which is greatervalues of R1 and R2 to know which is greater(E) It is different for each connection, but one must know the (E) It is different for each connection, but one must know the

value of value of to know which is greater. to know which is greater.

Junction RuleJunction Rule KirchoffKirchoff’’s 1st rule is also called the s 1st rule is also called the ““junction ruljunction rul

ee””..

The sum of the currents entering a junction The sum of the currents entering a junction equals the sum of the currents leaving the equals the sum of the currents leaving the junction.junction.

This rule is based upon conservation of charge.This rule is based upon conservation of charge.

Amount of current flowing in any direction is Amount of current flowing in any direction is proportional to the rersistance along the pathproportional to the rersistance along the path

iClickeriClicker

When there is a steady current in the circuit, the When there is a steady current in the circuit, the amount of charge passing a point per unit of time is amount of charge passing a point per unit of time is

(A) the same everywhere in the circuit(A) the same everywhere in the circuit (B) greater at point X than at point Y(B) greater at point X than at point Y(C) greater in the 1 (C) greater in the 1 resistor than in the 2 resistor than in the 2 resistor resistor(D) greater in the 1 (D) greater in the 1 resistor than in the 3 resistor than in the 3 resistor resistor(E) greater in the 2 (E) greater in the 2 resistor than in the 3 resistor than in the 3 resistor resistor

Loop RuleLoop Rule

KirchoffKirchoff’’s 2nd rule is also referred to s 2nd rule is also referred to as the as the ““loop ruleloop rule””..

The net change in electrical The net change in electrical potential in going around one potential in going around one complete loop in a circuit is equal to complete loop in a circuit is equal to zero.zero.

iClickeriClicker

KirchhoffKirchhoff’’s loop rule for circuit s loop rule for circuit analysis is an expression of which of analysis is an expression of which of the following?the following?

(A) Conservation of charge (A) Conservation of charge (B) Conservation of energy (B) Conservation of energy (C) Ampere's law (C) Ampere's law (D) Faraday's law (D) Faraday's law (E) Ohm's law (E) Ohm's law

OhmOhm’’s Law Graphs Law Graph Make a table of current and resistance data and graph the data Make a table of current and resistance data and graph the data

such that voltage is the slope of a best-fit line.such that voltage is the slope of a best-fit line.

Wire a circuit with a cell and one or more resistors.Wire a circuit with a cell and one or more resistors.

Calculate and record the resistance. Calculate and record the resistance.

Measure and record the corresponding current. Do this 5 times Measure and record the corresponding current. Do this 5 times without duplicating your resistance values. without duplicating your resistance values.

Rearrange the equation Rearrange the equation ΔΔV = IR so that V = IR so that ΔΔV is the slope of a linear V is the slope of a linear equation. equation.

Construct a graph from your data that corresponds to this Construct a graph from your data that corresponds to this rearranged equation. rearranged equation.

Calculate and clearly report the slope of the line. How does this Calculate and clearly report the slope of the line. How does this compare to the emf of 1.5 V for a D-cell?compare to the emf of 1.5 V for a D-cell?

Terminal VoltageTerminal Voltage

When a current is drawn from a battery, When a current is drawn from a battery, the voltage across its terminals drops the voltage across its terminals drops below its rated EMF.below its rated EMF.

The chemical reactions in the battery The chemical reactions in the battery cannot supply charge fast enough to cannot supply charge fast enough to maintain the full EMF.maintain the full EMF.

Thus the battery is said to have an Thus the battery is said to have an internal resistance, designated r.internal resistance, designated r.

Terminal Voltage and Terminal Voltage and EMFEMF

A real battery is then modeled as if it were a A real battery is then modeled as if it were a perfect emf, perfect emf, εε. in series with a resistor r.. in series with a resistor r.

Terminal voltage VTerminal voltage Vabab

When no current is drawn from the battery, When no current is drawn from the battery, the terminal voltage equals the emf.the terminal voltage equals the emf.

When a current I flows from the battery, When a current I flows from the battery, there is an internal drop in voltage equal to there is an internal drop in voltage equal to Ir, thus the terminal voltage (actual voltage Ir, thus the terminal voltage (actual voltage delivered) is Vdelivered) is Vabab = = εε - Ir - Ir

iClickeriClicker

In the circuit shown above, what is the value of the potential In the circuit shown above, what is the value of the potential difference between points X and Y if the 6‑volt battery has difference between points X and Y if the 6‑volt battery has no internal resistance? no internal resistance?

(A) 1 V (A) 1 V (B) 2 V (B) 2 V (C) 3 V (C) 3 V ( D) 4 V ( D) 4 V (E) 6V(E) 6V

iClickeriClicker

An immersion heater of resistance R converts An immersion heater of resistance R converts elec trical energy into thermal energy that is elec trical energy into thermal energy that is transferred to the liquid in which the heater transferred to the liquid in which the heater is immersed. If the current in the heater is is immersed. If the current in the heater is I, the thermal energy transferred to the I, the thermal energy transferred to the liquid in time t is liquid in time t is

(A) Irt (A) Irt (B) I2Rt (B) I2Rt (C) IR2t (C) IR2t (D) IRt2 (D) IRt2 (E) IR/t (E) IR/t