electricity - 10. DC Circuits

Question 1

electric current is a flow of charge carriers

charge on charge carriers is quantised

Question 2

equations

Answer 2

-Q = It
- for a current-carrying conductor, the expression I = Anvq or Anve, where n is the number density of charge carriers/FREE electrons

• V = W / Q
• P = VI,
  -P = I^2R
  -P = V 2 / R

-Lost volts = e.m.f − terminal p.d

-Lost volts = I × r (Ohm’s law)

–emf= IR + Ir
= I(R+r) (terminal pd + lost volts)

-I = I1 + I2+ I3 (first law - charge)

• emf1 + emf2 = V1 + V2 (2nd law - energy)

-Vout = R2/(R1+R2) x Vin
[R2 = resistance of the component you want to find the output voltage of.]

Question 3

potential difference across a component

Answer 3

the energy transferred per unit charge

Question 4

electromotive force

Answer 4

ENERGY TRANSFERRED

PER UNIT CHARGE

IN DRIVING CHARGE AROUND A COMPLETE CIRCUIT

Question 5

resistance
volt
coulomb

Answer 5

potential difference / current
joule per coulomb
ampere second

Question 6

Circuit Symbols (savemyexams)

most common

Answer 6

cell
potentiometer (resistor with right angle arrow pointing to middle)
variable resistor (penetrating arrow)
battery of cells
diode
thermistor
junction of conductors ( I.
switch
light-dependent resistor (point towards 2 arrows)
ammeter
voltmeter
lamp
capacitor (upside down T, below it another T)
fixed resistor
galvanometer (circle w upward arrow inside)
light-emitting diode (arrows pointing out)

Question 7

functions of most common components

1. switch

Answer 7

Turn the circuit on (closed)

or off (open)

Question 8

2. fixed resistor

Answer 8

resistor limits the flow of current.

A fixed resistor has a resistance it cannot change

Question 9

3. variable resistor

Answer 9

A resistor with a slider that can be used to change its resistance.

Used often in dimmer switches and volume controls

Question 10

4. thermistor (INVERSE)

Answer 10

resistance of a thermistor depends on its temperature.

As its temperature increases, its resistance decreases and vice versa

Question 11

5. light-dependent resistor

Answer 11

resistance of an LDR depends on the light intensity. As the light intensity increases, its resistance decreases and vice versa

Question 12

6. diode

Answer 12

A diode allows current to flow in one direction only.

-used to convert AC to DC current

Question 13

7. light-emitting diode LED

Answer 13

equivalent to a diode

-and emits light when a current passes through it.

• used for aviation lighting and displays (TVs, road signs)

Question 14

8. ammeter

Answer 14

Used to measure the current in a circuit.

Connected in series with other component

Question 15

9. voltmeter

Answer 15

Use to measure the potential difference of an electrical component.

• Connected in parallel with component

Question 16

uncommon circuit symbols

Answer 16

1. power supply —o o—
2. A.C. power supply —o ~ o—
3. heater (rectangle divided into 4)
4. motor (circle with M inside and ,—’ under)
5. generator (SQUARE with G inside)
6. earth (upside down T with 2 smaller lines under)
7. electric bell (top of circle semicircle on tree)
8. buzzer (bottom half of circle on tree)
9. microphone IO==
10. loudspeaker =□(sideways trapezium)
11. oscilloscope (circle with longer lone attached to down straight line then shorter tail)

Question 17

📍electromotive force

Answer 17

-charge pass thru power supply (eg battery) = gains energy

-emf: amount of energy transferred per coulomb of charge (C) when charge passes through a power supply

-energy drives the charge around the complete circuit and is transferred to the components

-emf =a measure of the energy transferred into the circuit by the power source

-emf =also the potential difference across the cell when no current is flowing

Question 18

emf (Volts)

Answer 18

energy transferred/charge

emf = W/Q

Question 19

how to measure emf

Answer 19

connecting a high-resistance voltmeter

around the terminals of the cell in an open circuit

Question 20

Emf & potential difference

Answer 20

-pd (/voltage) also the energy transferred per unit charge
-BUT potential difference is a measure of the energy transferred OUT of the circuit via the components
-V=W/Q
-When charge passes through a resistor, for example, energy is transferred from the charge (electron) to the resistor

The resistor therefore has a potential difference across it

Question 21

📍Internal resistance

Answer 21

📌All power supplies have some resistance between their terminals = internal resistance (lowercase r)

📌 internal resistance causes the charge circulating to dissipate some energy from the power supply itself = why the cell becomes warm after a period of time

📌 internal resistance therefore causes a loss of voltage or energy loss in a power supply
📌cell can be thought of as a source of e.m.f with an internal resistance connected in series

Question 22

circuit with emf

Answer 22

-VR is the terminal potential difference

This is the 📌voltage available in the circuit itself📌

Terminal p.d = I × R (Ohm’s law)

Question 23

what is VR and Vr
physics of it

Answer 23

-When a load resistor is connected, current flows through the cell and a potential difference develops across the internal resistance.
=> This voltage is not available to the rest of the circuit so is called the ‘lost volts’

-Vr is the lost volts. This is the voltage lost in the cell due to internal resistance, so, from conservation of energy:

Lost volts = e.m.f − terminal p.d

Lost volts = I × r (Ohm’s law)

Question 24

e.m.f
=the sum of these potential differences

so eqn

Answer 24

E = IR + Ir
= I(R+r)

so eg to find I = E/(R+r)

E=emf (V), I=current (A), R = load resistance (ohms), r = internal resistance

IR = terminal pd, Ir = lost volts

Question 25

📌📌📌kirchoff's first law (charge)

Answer 25

sum of current entering a junction equals sum of current leaving the same junction (ie algebraic sum of currents at a junction is zero)

Question 26

1st law

Answer 26

-consequence of conservation of charge - current shouldn’t decrease or increase in a circuit when it splits -In a circuit: A junction is a point where at least three circuit paths meet A branch is a path connecting two junctions -If a circuit splits into two branches, then the current before the circuit splits should be equal to the current after it has split - I = I1 + I2+ I3 charge is conserved on both sides of the junction -in series same at every point -In a parallel circuit, the current divides at the junctions and each branch has a different value. Kirchhoff’s first law applies at each junction EACH BRANCH HAS DIFF VALUE TIP: Junctions only appear in parallel circuits, and as circuits become more complex, it can be confusing as to which currents are into the junction and which are out. Drawing arrows on the diagram for the current flow (making sure it’s from positive to negative) at each junction like in the worked example will help with this.

Question 27

📌📌📌kirchoff's second law (energy)

Answer 27

algebraic sum of the pds and emfs is zero around a closed loop (ie sum of emfs equals sum of pds around a closed loop)

Question 28

2nd law

Answer 28

- consequence of conservation of energy - energy transferred into the circuit is equal to the energy transferred out of the circuit - emf1 + emf2 = V1 + V2 -sum of the potential difference across the individual components is equal to the sum of the e.m.f supplied by the batteries -In a series circuit, the potential difference is split across all components depending on their resistance = && sum of the potential difference across each component is equal to the total e.m.f of the power supply -In a parallel circuit, the potential difference is the same across each closed loop && sum of the potential difference in each closed circuit loop is equal to the total e.m.f of the power supply: -closed circuit loop acts as its own independent series circuit and each one separates at a junction. A parallel circuit is made up of two or more of these loops -makes parallel circuits incredibly useful for home wiring systems. A single power source supplies all lights and appliances with the same potential difference If one light breaks, current can still flow through the rest of the lights and appliances

Question 29

📍Resistors in Series Deriving the equation for resistors in series

Answer 29

-In a series circuit, the combined resistance of two or more resistors is the sum of the individual resistances In a series circuit: The current is the same through all resistors The potential difference is shared between all the resistors => from kirchoff's 1st law current thru each resistor is same since connected in series so no junctions => from kirchoff's 2nd law: total pd of both resistors in closed circuit loop must = sum of pds (pd across single resistor) so V = V1 + V2 -from ohm's law, pd is IR = IR1 + IR2 -since current is same for all resistors, divide by I -eqn extended showing you just add em

Question 30

summary When two or more components are connected in series:

Answer 30

combined resistance of the components is equal to the sum of the individual resistances

Question 31

DERIVATION R = R1 + R2 + R3 + ...

Answer 31

V = V1 + V2 IR = IR1 + IR2 R = R1 + R2 therefore R = R1 + R2 + R3 + ...

Question 32

📍Resistors in Parallel Deriving the equation for resistors in parallel

Answer 32

- parallel circuit, the reciprocal of the combined resistance of two or more resistors is the sum of the reciprocal of the individual resistances -in parallel: The current is split at the junction (and therefore between resistors) The potential difference is the same through all resistors -1st law: current thru each resistor will be diff bc current splits at junction. current thru equivalent resistor R will be total current I = I1 +I2 -2nd law: pd across each resistor in diff branches is same resistor R will have same pd across it too. V = V1 = V2 -ohm's law: I = V/R so V/R = V/R1 + V/R2 -since pd is same for all resistors divide by V -answer

Question 33

summary When two or components are connected in parallel:

Answer 33

reciprocal of the combined resistance is the sum of the reciprocals of the individual resistances +also resistors connected in parallel have SAME VOLTAGE -IN PARALLEL THE EQN means the combined resistance decreases and is less than the resistance of any of the individual components For example, If two resistors of equal resistance are connected in parallel, then the combined resistance will halve

Question 34

📌📌📌DERIVATION 1/R = 1/R1 + 1/R2 + 1/R3 + ...

Answer 34

I = I1 + I2 V = V1 = V2 I = V/R so V/R = V/R1 + V/R2 1/R = 1/R1 + 1/R2 ans --rmbr to do 1/ans finding R in parallel

Question 35

📍📍📍📍 POTENTIAL DIVIDERS

Answer 35

-two resistors are connected in series, through Kirchhoff’s Second Law, the potential difference across the power source is DIVIDED between them -Potential dividers are circuits which produce an OUTPUT voltage AS A FRACTION of its input voltage -Potential dividers have three main purposes: [3] 1. To provide a variable potential difference 2. To enable a specific potential difference to be chosen 3. To split the potential difference of a power source between two or more components -potential dividers used widely in volume controls and sensory circuits using LDRs and thermistors -Potential divider circuits are based on the ratio of voltage between components. This is equal to the ratio of the resistances of the resistors in the diagram below, giving the following equation: 📌Vout = R2/(R1+R2) x Vin -resistance R2 on the numerator of the fraction is always the resistance of the component that Vout is connected to

Question 36

what is what in a potential divider circuit

Answer 36

📌resistance R2 on the numerator of the fraction is always the resistance of the component that Vout is connected to 📌 input voltage Vin is applied to the top and bottom of the series resistors 📌output voltage Vout is measured from the centre to the bottom of resistor R2 📌The potential difference V across each resistor depends upon its resistance R: The resistor with the largest resistance will have a greater potential difference than the other one from V = IR If the resistance of one of the resistors is increased, it will get a greater share of the potential difference, whilst the other resistor will get a smaller share -In potential divider circuits, the p.d across a component is proportional to its resistance from V = IR

Question 37

📌📌Potentiometer

Answer 37

-similar to a variable resistor connected as a potential divider to give a continuously variable output voltage -can be used as a means of comparing potential differences in different parts of the circuit -circuit symbol is recognised by an arrow next to the resistor