4.2: Energy, Power, and Resistance

What is resistance

Opposition to flow of electric current in component

Definition of resistance

The resistance of a component is the voltage across the component divided by the current flowing through the component

Equation for resistance

V=IR

Ohm as a unit

1 Ohm is the resistance of a component when a potential difference of 1 volt is produced per ampere of current

Ohm’s Law Definition

For a metallic conductor at a constant temperature, the current in the conductor is directly proportional to the potential difference across the component

Temperature and resistance

In a circuit, the current will decrease over time because the heating caused by the current causes the temperature of the wire to increase over time, which increases the resistance over time.

Microscopic explanation of resistance

• Temp wire increases

• Positive ions inside wire have more internal frequency

• Vibrate with a greater amplitude

• Frequency of collisions between the charge carriers and metal ions increases

• More energy is transferred from the electrons, which heats the wire

What is an Ohmic component

Component that follows Ohm’s Law

I-V Characteristics: Resistor

• Opposes flow of current

• P.D directly proportional to current

• Ohmic component

• Resistance always constant

• Behaves same way despite polarity

I-V Characteristics: (Filament) Lamp

• Emits light

• P.D and current aren’t directly proportional

• Doesn’t obey Ohm’s law

• Resistance isn’t constant

• Behaves the same way despite polarity

I-V Characteristics: Diode/LED

• Allows current to flow in one direction

• Used in standby circuits

• P.D and current are not directly proportional

• Behaviour depends on polarity

• Resistance isn’t constant

• Doesn’t obey Ohm’s Law

I-V Characteristics: Thermistor

• Changes resistance depending on temperature

• Used in thermostats

• As the temperature increases, the resistance decreases

• used to monitor temp in ovens and engines, and to measure temperature in electrical devices

• NEGATIVE TEMPERATURE COEFFICIENT

I-V Characteristics: Light Dependent Resistor (LDR)

• Allows us to monitor light intensity of surroundings

• Made of semiconductors

• Used in smart phones to detect surrounding light

• Resistance decreases as light intensity increases

Negative Temperature Coefficient (NTC)

Property of materials that experience a decrease in electrical resistance when the temperature is raised

(Example of a component is a thermistor)

Positive Temperature Coefficient (PTC)

Refers to materials that experience an increase of electrical resistance when their temperature is changed

Method to determine I-V Characteristics

1. Set up components in one of the circuits (see f/c in fact sheet pack)

2. Add ammeter in series and voltmeter in parallel

3. Alter resistance (w variable resistor or potentiometer) to obtain a range of voltages across and currents through the component

4. Repeat readings several times (ensures reliable results)

   1. Plot a graph with current on y-axis and voltage on x-axis

What is resistivity

A constant used to remove the proportionality between 1) length and resistance and 2) ross sectional area and resistance

Equation for resistivity

R=pL/A

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R= resistance (Ω)

p= resistivity (Ωm)

A= cross sectional area (m²)

L= length (m)

How resistivity is defined

Resistance multiplied by cross sectional area divided by length, at a constant temperature

Variation of resistivity with temperature

Conductors: Resistivity increases with an increase in temp (PTC)

Insulators and semiconductors: Resistivity decreases with increase in temp (NTC)

Method for determining resistivity

1. Measure diameter of the wire with a micrometer at multiple places along the wire and find and average

2. Determine area of wire using A=πr²

3. Using circuit attached measure the current and P.D for various different lengths (regular intervals, measured with by a ruler)

4. Calculate resistance for each length R=V/I

5. Plot a resistance against length and graph and use y=mx+c analysis to determine resistivity

6. Multiply by gradient by cross-sectional area to determine resistivity

Definition of Power

Power is the rate of energy transfer

Unit of Power

Watts, W

Equation for Power with electrical energy tansferred

P=W/t

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W= electrical energy transferred (J)

t= time (which energy is being transferred) (s)

Equation for Power with Voltage

P=VI

---

V= potential difference (V)
I= current (A)

Equation for Power with current²

P=I²R

---

R= resistance (Ω)

I= current (A)

Equation for Power with voltage²

P=V²/R

---

V= potential difference (V)

R= resistance (Ω)

Equation for calculating energy transferred in a given time

W=VIt

---

W= electrical energy transferred (J)

t= time (s)

V= P.D (V)

I= current (A)

What is the Volt?

A reading that indicates energy transfers across a circuit

What determined the type of energy transfers across a circuit/component?

If the voltage measures a potential difference or electromotive force

Required definition for the volt

One volt is measured across a component when one Joule of energy is transferred per one Coulomb of charge passing through the component

The voltmeter

• Measures P.D

• Always in parallel

  • Ideal: has infinite resistance, so no current passes through it

Potential difference definition

The energy transferred from electrical energy to other forms per unit of charge (Volts)

Equation for potential difference

W=VQ

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W= energy transferred by charge Q (J)

V= potential difference (V)

Q= charge (C)

potential difference measures

Electrical energy lost in a circuit

Potential difference location

Across a component

Energy transfer of potential difference

Electrical —> something else

Electromotive force (emf) definition

Energy transferred from a source to electrical energy from some other form per unit charge (volts)

Equation for emf

W=εQ

---

W= energy transferred by charge (Q)

ε= electromotive force (V)

Q= charge (C)

EMF measures

Electrical energy gained in a circuit

Where emf is found

The power supply

Energy transfer of emf

Some other store —> electrical energy

Equation of energy transfer for charged particles

eV=1/2mv²

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e= elementary charge for required particle (C)

V= potential difference (V)

m= mass for required particle (kg)

v= velocity of particle (ms^-1)

What is an electron gun

An electrical device used to produce a narrow beam of electrons

How an electron gun works

A small metallic filament is heated by an electric current. Some of this fives some electrons enough energy to escape the surface of the metal (in a process called thermionic emission)

Thermionic emission

The emission of electrons through the action of heat

What happens when filament of electron gun is placed om a vacuum with a high potential difference that is applied between the filament and the anode

The filament acts as a cathode and free electrons accelerate towards the anode gaining kinetic energy. If the anode has a small hole in it, then electrons in line with this hole can pass through it (creating a beam of electrons)

The kilowatt-hour

• Unit of energy

• Utility companies measure the electrical energy you use in kWh

Definition of kWh

1 kilowatt-hour is the energy transferred by a device of power rating 1kW in the time of 1 hour

Calculating cost of energy

Cost (pence) = number of kWh used x cost of each kWh (pence)

Distinction between P.D and emf

• P.D is loss of electrical energy whereas emf is the gain of electrical energy

• P.D happens across components whereas emf happens across the power source

Linear Particle Acceleration (LINAC)

• Uses series of cylindrical electrodes to accelerate subatomic particles

• The polarity of the drift tube is altered between the +ve and -ve with precise timing so that as the protons leave the tube, polarity changes so they’re attracted to the next one