1

Basic Circuits Notes- THEORY NAME:________________________________________ An electrical circuit is a closed loop conducting path in which electrical current flows

Mechanical Component

Electrical Component

Purpose Assists or Impedes Flow

Pump Increases Pressure- Increases Energy/unit of working fluid

Pipes

Water Wheel

Water Working “fluid” NA

Now how does a circuit work?

In order to get the water flowing, you’d need a pump to increase the pressure of the water. Similarly, chemical reactions in the battery increase the electrical pressure on the electrons (the working fluid in an electrical circuit) allowing the electrons to flow through the elements of the circuit. Without this increase in pressure (electric potential/voltage), nothing would flow. The water is impeded a bit by friction with the pipe and event its own viscosity but really experiences resistance to flow when it encounters the water wheel. Similarly, as the electrons travel, they experience resistance to their flow imposed by the wires (pipes), generating heat— especially in the light bulb with the tiny, tiny wire that acts as a filament, it gets so hot that it creates light. (incandescence).

2

Component #1: Battery/ Power Source- Powers the external circuit ( by creating an electrical potential difference between the terminals of the battery/ power supply) SCHEMATIC FOR A 2 CELL BATTERY ( The long line indicates a “+” side or anode and the short line, the “-“ side or cathode)

QUESTIONS

1. Why are electrons (negative charges) and not protons (positive charges) the working fluid in our electrical circuit?

2. Ok, so if electrons are the charges traveling, then why is the flow of the electrical current going from positive to negative in the electrical circuit sketch on the previous page?

Current, I (units are Amperes, A)- the rate at which electrons flow past a given point in a circuit.

Electrical Resistance, R (units are Ohms, Ω)- is the opposition to the electron flow- happens throughout the circuit

Component #2: The Wire- pathway for the electrons

Electrons are the working fluid of the circuit

Resistance of a wire, Rwire varies: __________ (direct/inversely) with length, L ___________ (direct/inversely) with the cross-sectional area, A) ____________ with the difficulty of movement along the path (called resistivity, ρ – a consequence of material properties and where it falls in terms of conductivity) * Temperature also affects resistivity

For electronic circuit, using a cell is OK but not in Regents Physics

SCHEMATIC SYMBOL FOR A WIRE

3

Component #3: Load/ Device- what you hookup to the battery in order to do something useful with the energy supplied by the battery

There is a drop in electric potential energy and therefore, electric potential due to the impedance in the device

Voltage, V (units are volts,v)- Energy/unit charge at a given point in a circuit relative to another point in the circuit. 0 Volts is usually referenced at the point just before the current enters the battery. We usually care about the voltage difference across a device or any two points in a circuit- and will use a voltmeter to measure voltage.

Voltage versus Current- What’s the difference? Back to a Mechanical Analogy

FOR ENGINEERING, YOU WILL MOSTLY BE CONCERNED WITH DIAMETER OF THE CROSSECTION CALLED THE GUAGE OF THE WIRE- The smaller the diameter, the higher the gauge

In the diagram at the left, the height of the water in the tank is proportionate to the pressure of the water. The higher the water level, the higher the pressure of the water and this can be thought of as voltage. So using this analogy, pressure can be thought of as voltage and the flow of the water can be thought of as current.

4

HERE’S THE BIG ONE- VOLTAGE, CURRENT, AND RESISTANCE ARE RELATED USING OHM’S LAW OHM’S LAW:

Resistance= 𝑽𝑶𝑳𝑻𝑨𝑮𝑬 𝑫𝑰𝑭𝑭𝑬𝑹𝑬𝑵𝑪𝑬

𝑪𝑼𝑹𝑹𝑬𝑵𝑻 or R=

𝜟𝑽

𝜟𝑰 (unit of Resistance is the ohm, Ω)

Given any 2 variables, you can always find the third!

Class Problem 1: A 6.0 volt battery is attached to a light bulb that requires 0.9 A current. What is its Resistance? Class Problem 2: 20 milliamps (20mA) flows through a bulb with a resistance of 58 Ohms (58 Ω), what is the voltage drop across the bulb? Finally, Electrical Power, P (units Watts, W or Joules/sec, J/s) can be found using P= Current x Voltage Difference= I ΔV or = Current 2 x Resistance= I2 R or

= Voltage2/Resistance= 𝐕𝟐

𝐑

Electrical Energy or Work, W (unit is the Joule, J)= Electrical Power x time= P Δt

5

Class Problem 3: A lamp operates on 2A running on a 120 volt line,

(a) What is the power of the lamp? (b) What energy is consumed if the bulb is lit for 60 seconds? What about if it is on for 1minute? What if it is on for 20 hours? Class Problem 4: A bulb on a 120V is using 60 W, what is the resistance of the bulb? Circuits: TWO BASIC TYPES

How are these circuits different?

Lamp 1 Lamp 2

Lamp 3

Lamp 1

Lamp 2

Lamp 3

Circuit A Circuit B

Influencing the Flow Rate on a Tollway-The Toll Booth Analogy

6

BASIC TYPE #1: THE SERIES CIRCUIT A circuit where the current has only one path and must travel through all devices before returning to the battery

CURRENT REMAINS THE SAME 𝐼1 = 𝐼2 = 𝐼3 = ⋯ = 𝐼𝑛 KIRCHHOFF’S VOLTAGE LAW (KVL) : The sum of the voltage gains= sum of the voltage drops for any given loop OR

∑ 𝑉𝑑𝑟𝑜𝑝 𝑖

𝑛

𝑖=1

= ∑ 𝑉𝑔𝑎𝑖𝑛 𝑖

𝑛

𝑖=1

∆𝑉1 + ∆𝑉2 + ∆𝑉3 + ⋯ + ∆𝑉𝑛 = 𝑉𝐵𝑎𝑡𝑡𝑒𝑟𝑦 and Resistances add

𝑅1 + 𝑅2 + 𝑅3 + ⋯ + 𝑅𝑛 = 𝑅𝑇𝑜𝑡𝑎𝑙

Class Problem 5: Three 20 Ω resistors are placed in series with a 12 volt battery. Find

(a) The total Resistance (b) The current flowing through each resistor (c) The voltage drop across each resistor (d) The total power being used by the circuit

Series Circuit is…

Series Circuit- A circuit where the current has only one path and must travel through all devices before returning to the battery

Lamp 1 Lamp 2

Lamp 3 The current is the same

at any point in the

circuit, so

7

BASIC TYPE #2: THE PARALLEL CIRCUIT Voltage drop across each branch in parallel is the same and equal to the voltage of the power source

𝛥𝑉1 = 𝛥𝑉2 = 𝛥𝑉3 = ⋯ = 𝛥𝑉𝑛

𝐼1 + 𝐼2 + 𝐼3 + ⋯ + 𝐼𝑛 = 𝐼𝑇𝑜𝑡𝑎𝑙

As a result of having more paths, the total resistance is now reduced so that it is smaller than the smallest resistor in parallel

1

𝑅1+

1

𝑅2+

1

𝑅3+ ⋯ +

1

𝑅𝑛=

1

𝑅 𝑇𝑜𝑡𝑎𝑙

WARNING: BY ADDING MORE RESISTORS IN PARALLEL, YOU ARE GIVING THE CURRENT MORE PATHWAYS AND THIS CAN LEAD TO A HIGH TOTAL CURRENT

Class Problem 6: Three 20 Ω resistors are placed in parallel with a 12 volt battery. Find

(a) The total Resistance (b) The current flowing through each resistor (c) The voltage drop across each resistor (d) The total power being used by the circuit

KIRCHHOFF’S CURRENT LAW (KCL)- The amount of current flowing into any junction is equal to the amount flowing out of that junction

How are these circuits different?

Lamp 1 Lamp 2

Lamp 3

Lamp 1

Lamp 2

Lamp 3

Circuit A Circuit B

New Terminology • Node/junction- a connection or terminal

within a circuit where 2 or more elements are connected or joined together giving a connection point btw 2 or more branches

• Loop-A closed path in a circuit in which no

circuit element or node is encountered more than once

• Branch- part of a circuit where a component

or groups of components are connected btw 2 nodes

8

A NOTE ON REAL BATTERIES! Terminal Voltage: Terminal Voltage is the voltage the external circuit sees when a battery is being used. All batteries have internal resistance that becomes apparent when it is used in a circuit.

VTerminal = IR = – Ir or I = where = emf (marked battery voltage- Nominal Voltage)and r = internal

resistance of the battery. When charging a battery: VTerm = + Ir

Nominal Voltage- The “named” voltage- will be the voltage stamped on the battery without a load (external circuit on it) – close to what you would measure with a voltmeter

*Taken from Practical Electronics for Inventors, 4th Edition, pg 289 of Kindle Edition Class Problem 7: If a battery that is marked at 6V (nominal voltage) is connected to a 330kΩ load and the voltage reading across the external circuit is 5.8V, find the internal resistance of the battery.

R + r

X-Sectional View of a Wire Before a Battery Connected to the Circuit X-Sectional View of a Wire After a Battery

Connected to the Circuit

The terminal voltage, Vterm is the potential difference that the external circuit “sees” This would be the potential difference Vad for the circuit to the left

9

BASIC ELECTRICAL METERS

In lab, you will be using a digital multimeter which is an electrical meter that can act as many meters in one. This is great but you must remember a few things when using a multimeter. Two of your basic uses-Ammeter and Voltmeter mode An Ammeter measures current. A Voltmeter measures voltage differences FOR A REFRESHER ON HOW TO USE A MULTIMETER AS AN AMMETER, VOLTMETER,

OHMMETER, AND TO CHECK FOR CONTINUITY- Check out this video: Collin's Awesome How to Use a Multimeter You will use the multimeter in

o Ammeter Mode o Voltmeter Mode o Ohmmeter Mode o To Check for Continuity (That there is a conductive path aka closed circuit)

* There are more modes- feel free to look them up online & use

SCHEMATIC SYMBOL FOR AN AMMETER

SCHEMATIC SYMBOL FOR A VOLTMETER

10

SETTING UP THE METER Attach Probes into the proper jacks for your measuring purpose & SELECT A PROPER Range- Always start on the high end of the range and then work your way down when measuring! * For Example - If you need to measure 5Volts, set up for voltmeter mode and select the 20V range

INSERTING THE METER- HOW YOU INSERT A METER INTO A CRCUIT MATTERS! 1. AMMETER MODE TO MEASURE CURRENT-AFTER SWIITCHING OFF POWER SOURCE, “OPEN” THE CIRCUIT TO PLACE AN AMMETER to measure current through a device or part of the circuit. This is called placing your meter in series with what ever element you are measuring. Then, Turn circuit on for your measurement.

11

2. VOLTMETER MODE TO MEASURE VOLTAGE DIFFERENECE- THE CIRCUIT CAN BE “ON” WHEN YOU INSERT VOLTMETERS “ACROSS” WHATEVER YOU ARE TRYING TO MEASURE This is called placing the meter in parallel to whatever part of the circuit you are measuring

3. IN OHMMETER MODE TO MEASURE RESISTANCE- - TURN YOUR POWER SUPPLY OFF & KEEP IT OFF FOR THE MEASUREMENT and then-Connect one of your multimeter's probes to each side of the object whose resistance you want to measure. Resistance is always positive and the same in both directions, so it does not matter if you switch the black and red probes in this case (unless you are dealing with a diode, which acts like a one-way valve for electricity, so it has a high resistance in one direction and a low resistance in the other direction).

12

4. TO MEASURE CONTINUITY- TURN YOUR POWER SUPPLY OFF & KEEP IT OFF FOR THE MEASUREMENT and then-Touch two parts of your circuit with the probes. If the two parts of the circuit are electrically connected with very little resistance between them, your multimeter should beep. If they are not connected, it will not make a noise and might display something on the screen such as "OL," "OVER," or "1," which all stand for "overload."

13

The Voltage Divider- A very important circuit used in many places - like a potentiometer, inputs for comparators like in a 555 timer IC. You would use a voltage divider any time you need to decrease an output voltage Vout to a fraction of the input voltage Vin.

𝑽𝒐𝒍𝒕𝒂𝒈𝒆 𝒐𝒖𝒕 =𝑹𝒆𝒔𝒊𝒔𝒕𝒂𝒏𝒄𝒆𝟐

𝑹𝒆𝒔𝒊𝒔𝒕𝒂𝒏𝒄𝒆𝟏+𝑹𝒆𝒔𝒊𝒔𝒕𝒂𝒏𝒄𝒆𝟐𝑽𝒐𝒍𝒕𝒂𝒈𝒆𝒊𝒏

𝑽 𝒐𝒖𝒕 =𝑹𝟐

𝑹𝟏 + 𝑹𝟐𝑽𝒊𝒏

Class Problem # 8

Vin

+

-

𝑅1

𝑅2 Vout

A

C

B