4) Electric Circuits: Resistance and Energy

Switch open...

- no reading on V1, - V2 = the emf.

Consider the values given for the circuits and decide which circuit has the higher resistance.

Circuit A needs 3 Joules energy per Coulomb to sustain a rate of 2 Coulomb per second. Circuit B needs 4 Joules energy per Coulomb to sustain the same rate of charge flow as circuit A. B therefore has a higher resistance, as more energy is required.

Consider the values given for the circuits and decide which circuit has the higher resistance. (2)

In circuit A 4 Joules energy per coulomb can sustain a rate of 2 Coulombs per second. Where the same amount of energy in B sustains a higher rate of charge flow. A therefore has the higher resistance.

Resistance:

Resistance is the quotient of potential difference across a resistor and current passing through that resistor. Resistance is a material's opposition to the flow of electric current

An ohm is equivalent to:

V·A⁻¹

By considering the voltage and power rating of the light bulb, we can calculate

the resistance of the bulb and the amount of current it can sustain.

SPECIFICATIONS ON APPLIANCES Appliances have - potential difference (voltage) - power consumption (watt) In South Africa our household supplies deliver energy at ____. When one buys a light bulb that is rated as 60W, it means that...

± 240 V it will consume 60 J energy per second if connected to a 240 V supply.

Different materials have different resistances. How do you increase the resistance of a conductor?

- Heating the conductor, - increasing its length - or decreasing its thickness can increase the resistance.

*NB* The rules for solving circuit problems can be summarised as follows:

- Resistors in series divide potential difference in the same ratio as the resistance values, but the current through the resistors are the same. - Resistors in parallel divide current with the bigger current through the smaller resistor, but the potential difference across each is the same. - The effective resistance for resistors in series is the sum of the resistances. - The effective resistance for resistors in parallel is smaller than the smallest one.

Switch closed

- both V1 and V2 read the difference between the emf and the energy lost in the cell. The reading on V2 when the switch is open should ∴ = the sum of the lost volts and the potential difference across R when the switch is closed. emf = V + voltage lost in cell emf = Vload + Vinternal resistance emf = V +Ir

Parallel Resistors 1) Add a resistor in parallel 2) Remove a resistor in parallel 3) Increase the value of a resistor in parallel 4) Decrease the value of a resistor (rheostat) in parallel

1) Reff decreases 2) Reff increases 3) Refff increases 4) Reff decreases

USEFUL CIRCUIT PRINCIPLES Series resistors 1) Add a resistor in series 2) Remove a resistor in series 3) Increase the value of a resistor in series 4) Decrease the value of a resistor (rheostat) in series

1) Reff increases 2) Reff increases 3) Refff increases 4) Reff decreases

If the cell has an emf of 1,5 V and 0,2 V is required to move the charge through the cell, then there is only ___left for the rest of the circuit. --> the internal resistance of the cell can be viewed as ____. Potential difference is therefore ____ between the internal resistor and the resistors in the rest of the circuit.

1,3 V a resistor in series with the effective resistance of the rest of the circuit. divided

To generalise, the steps to take when comparing brightness / power are:

1. What effect has the change had on the total resistance of the circuit? Increase / Decrease / Stay same? 2. What effect does this have on the current in the main part of the circuit? For this we use: 3. Now look at the bulb in question and using one of the two power formulae & make a decision about the power / brightness.

For resistors in series, potential difference ____. For two resistors with resistances 2 Ω and 3 Ω, 15 V would divide as follows

2/5×15=6V (across the 2 Ω resistor) 3/5×15=9V (across the 3 Ω resistor.) This means that the potential differences are in the same ratio as the resistances.

I Ohm:

A conductor has a resistance of one ohm (1 Ω) when a potential difference of 1 volt maintains a current of one ampere in the conductor.

When is a conductor described as ohmic?

A conductor is described as ohmic when: - current is directly proportional to potential difference AND - the temperature remains constant.

If the temperature varies, is the conductor ohmic?

If the temperature varies, there is insufficient evidence to classify a conductor as "ohmic" or "not ohmic" e.g. in the case of a light bulb heating up, you cannot conclude that the light bulb is a non-ohmic conductor because the temperature is varying. All that you can say it that there is not a direct relationship between current and pd.)

b) Total resistance in the circuit

Internal r is in series with other resistors Rtotal = R + r = 6 + 0,1 = 6,1 Ω

Factors that affect resistance:

Length of resistor: The longer the length the greater the resistance Temperature: The greater the temperature the greater the resistance Thickness: The thicker the resistor the smaller the resistance Type of material: Different materials have different resistances

In general we use this equation when comparing bulbs in series because we know that the current at all points in a series circuit is the same.

P = I²R

What is in series and parallel in the following circuit

R1 is in parallel to the combination of R2 and R3 R2 and R3 are in series with each other. DO NOT say that R1 is parallel to R2 or that R1 is parallel to R3

What happens to the value of V when each of the following changes is made: - S1 is closed while S2 remains open and S3 closed - S2 is closed while S1 remains open and S3 closed - S3 is opened while S1 and S2 remain open

S1 closed - Reff becomes 0, so V becomes 0 S2 closed - Reff decreases, so V decreases S3 opens - Reff increases, so V increases

Consider the following two circuits. The same cell is used in both circuits.

Since they are the same cell, the Emf and r are the same in both circuits.

What if we have different values for all the quantities? either: - the higher potential difference represented the larger resistance. - the smaller current represented the larger resistance. always make the current 1 A.

The amount of V per A is therefore an indication of resistance. Where R = resistance in ohms (Ω) V = potential difference in volts I = current in amperes

Ohm's Law:

The current between any 2 points in a conductor is directly proportional to the potential difference applied across the points provided that the temperature remains constant.

SHORT CIRCUITS A short circuit can take on various forms. The first one is a direct connection between the two electrodes of a cell or battery with a connection wire.

The diagram shows the two poles of a cell connected with a connecting wire. This means that there would be a very great current in the circuit and that the cell would run flat in a very short period of time.

The power rating on an appliance is an indication of the...

The work done in the appliance per second

Emf and r are properties of a cell. How do they differ between circuit?

They do not change from one circuit to another if the cell remains the same.

Two resistors in series.

This circuit is identical to having one with only resistor B in it. The short therefore erases the effect of resistor A in the circuit.

What happens when too much current is drawn?

This current is much bigger than the current that the filament of the bulb can sustain. - The filament will therefore heat up beyond the temperature that it was designed for and burn out. (bulb is forced to consume more power than what it was designed to do.) Similarly one would find that if the bulb was connected to source with a lower voltage, the power consumption would be less than specified and it would not burn as brightly as it should.

The resistance of the connecting wire is negligible or almost 0. If the cell has an emf of 1,5 V and an internal resistance of 0,1 Ω, the following would happen:

This means that there is nothing of the emf left to be used in the external circuit. The potential difference is therefore "wiped out" by the short circuit. One can also short out certain components of a circuit by connecting a connecting wire parallel to them.

What happens to V in the following circuit when R increases (R is just Reff if there are more resistors in the circuit)

V INCREASES (2 explanations) 1) the emf divides between the effective resistance and the internal resistance in the same ratio as the resistance values because they're in series If Reff increases then V increases 2) emf = I(R + r) If R increases, I decreases but V = emf - Ir Because Ir decreases, V decreases

1. A circuit with one cell with emf 12V and internal resistance 0,1 Ω is connected to a resistor of 6 Ω. The switch is open. Calculate the: a) Reading on voltmeter

When the switch is open, no current flows through the circuit, therefore the voltmeter across the cell reads the emf i.e. 12 V

d) Reading on voltmeter

With the switch closed the voltmeter reads Vload . Vload = IR = (1,97)(6) = 11,8 V

Resistance is....

a material's opposition to the flow of electrical current.

The internal resistance in a cell dissipates energy when charge moves through the cell. The internal resistance of the cell is.... (how else can it be represented?)

a resistor in series with the effective resistance of the rest of the circuit.

Power is an indication of _____. If we wish to compare: - the brightness of two bulbs in a circuit, - or determine how the brightness of a bulb changes when changes are made to a circuit, we need to compare the power in the components.

brightness

This can be investigated using a ___ in Joule's experiment. By using his famous _____, Joule showed that the amount of energy transferred to water when heating can be calculated by ____.

calorimeter paddle-wheel apparatus q = mcΔT, where: cwater = 4200 Jkg⁻¹K⁻¹ and m = mass ΔT = temperature change of the water

Potential difference is directly proportional to the current in an ohmic resistor. Most conductors are ohmic between ____. Examples of conductors that are usually non-ohmic are: ____.

certain temperatures electric discharge through gases, con- duction through vacuum tubes, glass and germanium and elec- trolytes.

Conductors which obey Ohm's Law have a ____ when the voltage is varied across them or the current through them is increased. These conductors are called ohmic conductors. A graph of the current vs. the voltage across these conductors will be a straight-line through the origin. Some examples of ohmic conductors are _____

constant resistance circuit resistors and nichrome wire.

How the ammeter should be con- nected to measure current: In this arrangement the ammeter has to measure ____. That is why it is connected in series with the resistor. The ammeter has to have a ___ resistance compared to the resistor to not affect the reading.

current at a point very low

For resistors in parallel the potential difference across the resistors are the same and the current ____.

divides between the resistors.

To measure the potential difference across the resistor (between the points where the resistor is connected) in the circuit given: The voltmeter would have to be connected as shown above. This arrangement should not affect the ____ in the circuit. This means that the voltmeter should have a ____ resistance compared to the resistor to not affect the reading.

effective resistance very high

the effective resistance is very low (for two parallel resistors it is always less than the smallest).

equal to

Introducing resistance The physical properties of a conducting material influence the _____. The phenomenon that these properties could _____ is called resistance.

flow of charge through the material restrict the flow of charge

Batteries and cells have an internal resistance (r) which is measured in ohms (Ω). When electricity flows round a circuit the ____ of the cell itself resists the flow of current and so _____.

internal resistance thermal (heat) energy is wasted in the cell itself.

Constant temperature for Ohm's Law. This is because the resistance of some conductors changes as their temperature changes. These types of conductors are called ____. A _____ is a common example of a non-ohmic conductor. Other examples of non-ohmic conductors are _____

non-ohmic conductors, because they do not obey Ohm's Law. light bulb diodes and transistors.

MEASUREMENTS IN CIRCUITS Voltmeters measure ____ Ammeters measure ____ These meters are labelled so that the ____ To measure potential difference, the voltmeter has to be connected ___.

potential difference current positive terminal is connected to the positive side of the circuit and the negative terminal to the negative side. between two points

When the switch is closed, current flows and the reading on the voltmeter will be....

potential difference or Vload

When the switch is closed, current flows. The cell uses some of its energy (Emf ) to _____. This energy is not available to the circuit outside the cell (known as the external circuit) and is known as the.... The energy that is available to the external circuit is known as the _____

push charges through the cell "lost" volts or Vinternal resistance. potential difference or Vload

The cell in the diagram below has an internal resistance as shown. With the switch closed, V1 (across the resistor) is:

smaller than the emf.

By using the result obtained with the paddle-wheel apparatus, he could calculate the energy transferred to a known mass of water by measuring the _____.

temperature increase in the water. All three relationships were verified, and therefore the formula w = I²Rt was not rejected.

When the switch is open then no current flows. The reading on the voltmeter will be...

the Emf.

For resistors in parallel, current divides with ____. For a 2 Ω and 3 Ω, 15A would divide with...

the bigger current through the smaller resistor 9 A through the 2 Ω resistor and 6A through the 3 Ω resistor.

For some resistors, R is constant. This means that _____. We say that such resistors are ___ and that they obey Ohm's Law. If we represented this phenomenon graphically, it would show a direct proportion.

the current changes proportionally as the potential difference across the resistor is adjusted ohmic

The resistor in the circuit has a short over it. Because this relates to - two resistors in parallel - of which one has an almost zero resistance,

the effective resistance is very low (for two parallel resistors it is always less than the smallest).

The unit of measurement V·A-1 is

the ohm (Ω).

Microscopically we can describe resistance as follows. As elec- trons in the outer energy levels (valence electrons) move from one atom to the next, their movement is restricted by ____. These valence electrons are ____ (they don't belong in one spot only). Collisions between the delocalised electrons (current) and the other particles make the delocalised electrons loose, kinetic energy and therefore the ____ is affected and the number of particles passing any given point in one second becomes ___ than what it would have been.

the presence of all the other particles (there will be many other electrons to interact with) delocalised flow of charge less

Calculating effective resistance For series resistors, the potential difference across all the resistors is equal to ____. The ____ through series resistors is the same.

the sum of the potential differences across the individual resistors current

INTERNAL RESISTANCE OF A CELL The emf of a cell indicates ____. A cell also has internal resistance that ____ when charge moves through the cell.

the total amount of energy that the cell can supply per coulomb charge that moves through the cell. dissipates energy

Emf is measured in ____ (V) It is equal to the potential difference across the terminals of the cell when _____.

volts no current is flowing. (switch is open)

Modelling formulae for work and power in circuits From E fields we know: w = QV and Q = It. Combining yields W = VIt and P = VI. It is now possible to find four more equations. Two can be found by substituting V = IR into the above equations. This yields:

w=I²Rt and P=I²R