Chapter 18 & 19 Current, DC Circuits

Current is defined as the flow of positive charge. I = Q/t I: current in Amperes or Amps (A) Q: charge in Coulombs (C) t: time in seconds (s)

In a normal electrical circuit, it is the electrons that carry the charge. So if the electrons move this way, which way does the current move? Charge carriers

Sample problem How many electrons per hour flow past a point in a circuit if it bears 11.4 mA of direct current? If the electrons are moving north, in which direction is the current?

Circuit Components

Cell Cells convert chemical energy into electrical energy. The potential difference (voltage) provided by a cell is called its electromotive force (or emf). The emf of a cell is constant, until near the end of the cell’s useful lifetime. The emf is not really a force. It’s one of the biggest misnomers in physics! Battery A battery is composed of more than one cell in series. The emf of a battery is the sum of the emf’s of the cells.

Sample problem If a typical AA cell has an emf of 1.5 V, how much emf do 4 AA cells provide? Draw the battery composed of these 4 cells.

Circuit Components

Sample Problem: Draw a single loop circuit that contains a cell, a light bulb, and a switch. Label the components. Now put a voltmeter in the circuit so it reads the potential difference across the light bulb.

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

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

Sample Problem: Draw a circuit having a cell and four bulbs. Exactly two of the bulbs must be in parallel.

Draw a circuit containing one cell, one bulb, and a switch. Create this in the PhET simulation. Measure the voltage across the cell and across the bulb. What do you observe? Minilab #1

Draw a circuit containing two cells in series, one bulb, and a switch. Create this in the PhET simulation. What do you observe happens to the bulb (compared to minilab #1)? Measure the voltage across the battery and across the bulb. What do you observe? Minilab #2

Minilab #3 Draw a circuit containing two cells in series, two bulbs in series, and a switch. Create this in the PhET simulation. What do you observe happens to the bulbs when you disconnect one of the bulbs? ( or open the switch)? Measure the voltage across the battery and across each bulb. What do you observe?

Minilab #4 Draw a circuit containing two cells in series, two bulbs in parallel, and a switch right next to one of the bulbs. Create this in the PhET simulation. What do you observe happens to the bulbs when you disconnect one bulb (or open the switch)? Measure the voltage across the battery and across each bulb. What do you observe?

How does the voltage from a cell or battery get dispersed in a circuit… when there is one component? when there are two components in series? when there are two components in parallel? General Rules

Ohm’s Law and Resistivity

Conduct electricity easily. Have high “conductivity”. Have low “resistivity”. Metals are examples. Wires are made of conductors Conductors

Don’t conduct electricity easily. Have low “conductivity”. Have high “resistivity”. Rubber is an example. Insulators

Resistors are devices put in circuits to reduce the current flow. Resistors are built to provide a measured amount of “resistance” to electrical flow, and thus reduce the current.. Resistors

Draw a single loop circuit containing two resistors and a cell. Draw voltmeters across each component. Sample problem

Resistance depends on resistivity and on geometry of the resistor. R = ρL/A ρ: resistivity (Ω m) L: length of resistor (m) A: cross sectional area of resistor (m 2 ) Unit of resistance: Ohms (Ω) Analogy to flowing water Resistance, R

Resistivities (ρ) of common materials Silver 1.59 x Ωm Copper 1.72 x Ωm Aluminum 2.82 x Ωm Iron 10.0 x Ωm Nichrome 100 x Ωm Carbon 3500 x Ωm Drinking Water 2 x 10 2 Ωm Hard Rubber 1 x Ωm Air 1 x Ωm

Sample problem What is the resistivity of a substance which has a resistance of 1000Ω if the length of the material is 4.0cm and its cross sectional area is 0.20 cm 2 ?

Ohm’s Law Resistance in a component in a circuit causes potential to drop according to the equation: ΔV = IR ΔV: potential drop/difference (Volts) I: current (Amperes) R: resistance (Ohms) The drop in potential occurs as electrical energy is transformed to other forms (heat, light) and work is done.

Sample problem Determine the current through a 333Ω resistor if the voltage drop across the resistor is observed to be 1.5 V.

Sample problem Draw a circuit with a AA cell attached to a light bulb of resistance 4Ω. Determine the current through the bulb. (Calculate)

Power P = W/t P = ΔE/Δt P = I ΔV P: power (W) I: current (A, C/s) ΔV: potential difference (V, J/C) P = I 2 R P = (ΔV) 2 /R Units: Watts OR Joules/second

Sample problem How much current flows through a 100-W light bulb connected to a 120 V DC power supply? What is the resistance of the bulb?

Sample problem If electrical power is 5.54 cents per kilowatt hour, how much does it cost to run a 100 W light bulb for 24 hours?

Resistors in circuits Resistors can be placed in circuits in a variety of arrangements in order to control the current. Arranging resistors in series increases the resistance and causes the current to be reduced. Arranging resistors in parallel reduces the resistance and causes the current to increase. The overall resistance of a specific grouping of resistors is referred to as the equivalent resistance.

Resistors in series

Resistors in parallel R1R1 Individual currents add to total current Voltage drop is the same across each resistor

What is the equivalent resistance of a 100 Ω, a 330 Ω and a 560 Ω resistor when these are in a parallel arrangement? (Draw, build a circuit in PhET, measure, and calculate. Compare measured and calculated values.) Minilab #5

Set up your digital multi-meter to measure resistance. Measure the resistance of each of three light bulbs. Record the results. Wire the three bulbs together in series, and draw this arrangement. Measure the resistance of all three bulbs together in the series circuit. How does this compare to the resistance of the individual bulbs? Confirm measurement with a calculation. Wire the three bulbs together in parallel, and draw this arrangement. Measure the resistance of the parallel arrangement. How does this compare to the resistance of the individual bulbs? Confirm measurement with a calculation. Minilab #6

Draw and build an arrangement of resistance that uses both parallel and series arrangements for 5 or 6 resistors in your kit. Calculate and then measure the equivalent resistance. Compare the values. Minilab #8

Sample Problem Draw a circuit containing, in order (1) a 1.5 V cell, (2) a 100Ω resistor, (3) a 330 Ω resistor in parallel with a 100 Ω resistor (4) a 560 Ω resistor, and (5) a switch. a) Calculate the equivalent resistance. b) Calculate the current through the cell. c) Calculate the current through the 330Ω resistor.

Resistors in Series and in Parallel An analogy using water may be helpful in visualizing parallel circuits:

Kirchhoff’s Rules Some circuits cannot be broken down into series and parallel connections.

Kirchhoff’s 1 st Rule For these circuits we use Kirchhoff’s rules. Kirchhoff’s 1 st Rule, Junction rule: The sum of currents entering a junction equals the sum of the currents leaving it (conservation of charge).

Sample problem

Kirchhoff’s 2 nd Rule Loop rule: The sum of the changes (net change) in electrical potential around a closed loop in a circuit is equal to zero (conservation of energy).

Sample problem

Capacitance (Ch 17) A capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge and energy.

Capacitor Each conductor (plate) initially has zero net charge Electrons are transferred from one conductor to the other (charging the conductor) Equal charge magnitude and opposite sign, net charge is still zero When a capacitor has or stores charge Q, the conductor with the higher potential has charge +Q and the other -Q if Q>0

When a capacitor is connected to a battery, the charge on its plates is proportional to the voltage: (17-7) The quantity C is called the capacitance. Unit of capacitance: the farad ( F ) 1 F = 1 C / V

Examples 1.Calculate the capacitance of a parallel-plate capacitor whose plates are 20cm x 3 cm and are separated by a 1.0 mm air gap. 2. What is the charge on each plate if a 12.0V battery is connected across the two plates? 3. What is the electric field between the plates? 4. Estimate the area of the plates needed to achieve a capacitance of 1F, given the same air gap d.

17.7 Capacitance The capacitance does not depend on the voltage; it is a function of the geometry and materials of the capacitor. For a parallel-plate capacitor: (17-8)

17.9 Storage of Electric Energy A charged capacitor stores electric energy; the energy stored is equal to the work done to charge the capacitor. (17-10)

17.7 Capacitance Parallel-plate capacitor connected to battery.

19.5 Circuits Containing Capacitors in Series and in Parallel Capacitors in parallel have the same voltage across each one:

19.5 Circuits Containing Capacitors in Series and in Parallel In this case, the total capacitance is the sum: (19-5)

19.5 Circuits Containing Capacitors in Series and in Parallel Capacitors in series have the same charge:

19.5 Circuits Containing Capacitors in Series and in Parallel In this case, the reciprocals of the capacitances add to give the reciprocal of the equivalent capacitance: (19-6)

19.7 Electric Hazards Even very small currents – 10 to 100 mA can be dangerous, disrupting the nervous system. Larger currents may also cause burns. Household voltage can be lethal if you are wet and in good contact with the ground.

Ammeters and Voltmeters

Voltmeter A voltmeter measures voltage It is placed in the circuit in a parallel connection Measures potential difference, needs two points on either side of component A voltmeter has very high resistance, and therefore would contribute.

Ammeter

Measures Resistance. Placed across resistor when no current is flowing. Ohmmeter

19.1 EMF and Terminal Voltage Electric circuit needs battery or generator to produce current – these are called sources of emf. Battery is a nearly constant voltage source, but does have a small internal resistance, which reduces the actual voltage from the ideal emf: (19-1)

19.1 EMF and Terminal Voltage This resistance behaves as though it were in series with the emf.

Terminal Voltage and EMF When a current is drawn from a battery, the voltage across its terminals drops below its rated EMF. The chemical reactions in the battery cannot supply charge fast enough to maintain the full EMF. Thus the battery is said to have an internal resistance, designated r. Ex: Starting a car with the headlights on, the lights dim. The starter draws a large current and the battery voltage drops as a result.

Terminal Voltage and EMF A real battery is then modeled as if it were a perfect EMF Ɛ in series with a resistor r. Terminal voltage V ab When no current is drawn from the battery, the terminal voltage equals the EMF. When a current I flows from the battery, there is an internal drop in voltage equal to Ir, thus the terminal voltage (actual voltage delivered) is V ab = Ɛ - Ir

A battery whose EMF is 40V has an internal resistance of 5 ohms. If this battery is connected to a 15 ohm resistor R, what will the voltage drop across R be? 1.10 V 2.30 V 3.40 V 4.50V 5.70V

19.4 EMFs in Series and in Parallel; Charging a Battery EMFs in series in the same direction: total voltage is the sum of the separate voltages

19.4 EMFs in Series and in Parallel; Charging a Battery EMFs in series, opposite direction: total voltage is the difference, but the lower- voltage battery is charged.

19.4 EMFs in Series and in Parallel; Charging a Battery EMFs in parallel only make sense if the voltages are the same; this arrangement can produce more current than a single emf.