13.3 - emf + internal resistance

what is the internal resistance of?

the source

is there internal resistance in any other component or just the source?

just the source

what is the internal resistance of a source?

the loss of potential difference per unit current in the source when current passes through the source

the internal resistance is the loss of what?

potential difference per unit current

the internal resistance is the loss of potential different per what?

potential difference per unit current

the internal resistance is the loss of potential difference per unit current when what?

when current passes through the source

what is the internal resistance of a source due to?

opposition to the flow of charge through the source

what does opposition to the flow of charge through the source cause?

internal resistance of the source

what does internal resistance of the source cause?

electrical energy produced by the source to be dissipated inside the source when charge flows through it

what causes electrical energy produced by the source to be dissipated inside the source when charge flows through it?

internal resistance

what does internal resistance cause dissipation of?

electrical energy produced by the source

what does internal resistance cause electrical energy produced by the source?

dissipate it inside the source when charge flows through it

when is electrical energy dissipated inside the source?

• when there is internal resistance in the source

• when charge flows through the source

where is electric energy dissipated when there is internal resistance and charge is flowing through the source?

dissipated inside the source

what is the emf (electromotive force)?

energy transferred from chemical energy to electrical energy per coulomb of charge produced by the source

the emf is the energy transferred from what?

energy transferred from chemical energy to electrical energy

the emf is the energy transferred from chemical energy to electrical energy per what?

per unit coulomb of charge produced by the source

the emf is the energy transferred from chemical energy to electrical energy per unit coulomb of charge produced by what?

produced by the source

is there emf in any other component or just the source?

just the source

is the emf a force?

no, despite it’s name

what is the equation linking emf, electrical energy, and charge?

ε = E / Q

what is the pd across the terminals of the source?

the electrical energy per unit charge delivered by the source when it is in a circuit

the pd across the terminals of the source is the electric energy per what?

per unit charge delivered by the source

the pd across the terminals of the source is the electrical energy per unit charge delivered by the source providing what?

it is in the circuit

when is the terminal pd less than the emf?

whenever current passes through the source

when current passes through the source, which is larger - the terminal pd or the emf?

the emf

why is the emf larger than the terminal pd when current passes through the source?

because of the internal resistance of the source, since the internal resistance is the loss of pd per unit current when current passes through the source

what is the symbol for internal resistance?

r

what is the unit for internal resistances?

ohms Ω

how is internal resistance shown on a circuit diagram?

as a resistor in series and boxed with a cell or battery

here

circuit diagram for internal resistance here

internal resistance

for a series circuit containing internal resistance and a resistor, what is R_total? here

R_total = r + R

we treat it as we would treat any resistors in series

for a parallel circuit containing internal resistance and a resistor, what is R_total? here

1 / R_total = 1 / r + 1 / R

we treat it as we would treat any resistors in parallel

how do you find the total resistance when there is internal resistance?

by treating it the same way you’d treat multiple resistors in a circuit -

• when in series, R_total = r + R

• when in parallel, 1 / R_total = 1 / r + 1 / R

what is the equation linking emf, current, and resistance?

• ε = IR + Ir

• ε = I (R + r)

derive this equation - ε = I (R + r)

here

what is the lost pd inside the cell?

the pd across the internal resistance of the cell

lost pd inside the cell = ?

• the pd across the internal resistance of the cell

• the difference between the cell emf and the pd across its terminals

• energy per coulomb dissipated inside the cell due to its internal resistance

the lost pd inside the cell - define in terms of internal resistance

the pd across the internal resistance of the cell

the difference between the cell emf and the pd across its terminals - define in terms of energy

the energy per coulomb dissipated inside the cell due to its internal resistance

the difference between the cell emf and the pd across its terminals = ?

• the lost pd inside the cell

• the energy per coulomb dissipated inside the cell due to its internal resistance

the energy per coulomb dissipated inside the cell due to its internal resistance = ?

• the lost pd inside the cell

• the difference between the cell emf and the pd across its terminals

what is the power supplied by the cell?

• I ε = I²R + I²r

• the power delivered to R + the power wasted in the cell due to its internal resistance

what is the power delivered to R + the power wasted in the cell due to its internal resistance?

the power supplied by the cell

I ε = I²R + I²r - what is this equation for?

the power supplied by the cell

derive this equation - I ε = I²R + I²r

here

what does a power delivered to load vs load resistance graph look like?

here

• curved with increasing gradient until a peak when load resistance = internal resistance

• gradient becomes steeper with higher load resistance

what is the peak of a power delivered to load vs load resistance graph?

• maximum power delivered to the load

• load resistance = internal resistance of source

• load is matched to the source

when does a power delivered to load vs load resistance graph reach its peak?

when load resistance = internal resistance of source

when is the power delivered to the load at its maximum?

when the load resistance is equal to the internal resistance of the source

what happens when the load resistance is equal to the internal resistance of the source?

maximum power is delivered to the load

when is the load said to be matched to the source?

• when load resistance = internal resistance of the source

• at maximum power delivered to the load

how can you measure the potential difference across the terminals of a cell?

here

by connecting a high resistant voltmeter parallel to the terminals of the cell

what is the point of measuring the pd across the terminals of a cell?

to find internal resistance and emf

how do you find internal resistance using a circuit?

here

• measure the pd across the terminals of a cell when the cell is in a circuit

• adjust current using a variable resistor

• record the pd and current (using a voltmeter and ammeter, respectfully) and plot on a pd v current graph

• gradient = internal resistance

how do you find emf using a circuit?

• measure the pd across the terminals of a cell when the cell is in a circuit

• adjust current using a variable resistor

• record the pd and current (using a voltmeter and ammeter, respectfully) and plot on a pd v current graph

• y-int = emf

measuring pd across terminals of a cell here

measuring pd across terminals of a cell

what kind of voltmeter is used in this circuit?

here

a high resistance voltmeter

why is the voltmeter used in this circuit of a high resistance?

to prevent current going through it idk i’ll go through it

when measuring the pd across the terminals of a cell, does the cell need to be in a circuit?

yes

what is the point of the voltmeter in this circuit?

here

to measure the pd across the terminals of the cell

where does the voltmeter go in this circuit?

here

here

why is the voltmeter parallel to the cell in this circuit?

here

because it is measuring the pd across the terminals of the cell to be later used to find emf and internal resistance

where does the ammeter go in this circuit?

here

here

why is the ammeter in series with the cell in this circuit?

here

to measure the current in the circuit to be later used to find emf and internal resistance

• if it were in parallel with the cell, it wouldn’t be accurately measuring the current as each junction in a parallel circuit has a different current flowing through it

• if it were in parallel with the cell, it wouldn’t be measuring the current of the cell but the current of the circuit (i.e., past the resistors). we’re only interested in measurements for the cell

why is the ammeter directly after the cell in this circuit?

here

because it is measuring only the current of the cell rather than the circuit as a whole

what is the point of the terminal resistor in this circuit?

here

to vary the current, as current is the independent variable of this graph

here

what is the point of the lamp / resistor in this circuit?

here

to limit the maximum current that can pass through the cell

why do you need to do this? i think i get it but idk how to describe it

what graph does this circuit produce?

here

here

what is the equation of this graph?

here

V = ε - Ir

• V = potential difference across the terminals of the cell

• ε = emf

• I = current of the cell

• r = internal resistance

V = ε - Ir

here

which axis is the independent variable on?

x-axis

which axis is the dependent variable on?

y-axis

what is this graph for? here

• finding emf of the source

• finding internal resistance of the source

what is the x-axis of the graph produced by this circuit?

what is the y-axis of the graph produced by this circuit?

what is the gradient of the graph produced by this circuit?

is the gradient of the graph produced by this circuit positive or negative?

negative

why is the gradient of the graph produced by this circuit negative?

terminal pd decreases as the current increases because the lost pd increases (due to internal resistance) as the current increases

when current increases, what happens to terminal pd?

decreases

why does terminal pd decrease when current increases?

because the lost pd increases (due to internal resistance) as the current increases

when current increases, what happens to the lost pd?

increases

why does lost pd increase when current increases?

because of internal resistance

what is the shape of the graph produced by this circuit?

what is the independent variable of the graph produced by this circuit?

what is the dependent variable of the graph produced by this circuit?

what is the y-int of the graph produced by this circuit?

where is the internal resistance on the graph produced by this circuit?

where is the emf on the graph produced by this circuit?

where is the current of the source on the graph produced by this circuit?

where is the pd of the source on the graph produced by this circuit?

derive this equation - V = ε - Ir

here, circuit and graph and also equation derivation

V = ε - Ir - what does this equation tell you?

come back 2 this

why do we need multiple readings for current when finding emf and internal resistance?

• in order to plot a graph, as current is our independent variable, so the y-int (emf) and gradient (internal resistance) can be found

• to compare the terminal pd with different current values of the source

what is terminal pd?

potential difference across the terminals of a cell (i.e., pd of the source)

how do you find emf and internal resistance if the terminal pd at two different values of current is know?

here

r = (V₁ - V₂) / (I₂ - I₁)

the internal resistance for when the terminal pd is known for two different values of current

derive this equation - r = (V₁ - V₂) / (I₂ - I₁)

here

what are the correct numbers for this equation? - r = (V_a - V_b) / (I_c - I_d)

r = (V₁ - V₂) / (I₂ - I₁)

how can you calculate emf using this equation? - r = (V₁ - V₂) / (I₂ - I₁)

work out internal resistance, then substitute it into V = ε - Ir (for either terminal pd at a particular current) to find ε