C10. DC Electricity II

Question 1

Summarise Kirchhoff’s Second Law.

Answer 1

In any single closed loop of a circuit, the sum of electromotive forces is equal to the sum of potential differences.

Question 2

What can we say about current and potential difference in a series circuit?

Answer 2

Any series circuit has just one closed loop.
- By Kirchhoff’s 1st Law: current must stay constant throughout.
- By Kirchhoff’s 2nd Law: the total emf if shared proportionally between all of the components.

Question 3

What can we say about current and potential difference in a parallel circuit?

Answer 3

A parallel circuit provide more than one possible path for charges.
- By Kirchhoff’s 1st Law: the sum of currents entering a junction = current leaving. This is defined by resistance. The higher the resistance of a branch, the lower the current that flows through it for a given emf.
- By Kirchhoff’s 2nd Law: since sum of emfs = sum of pd in a closed loop, the total pd across each branch equals the input emf.

Question 4

If two identical components are connected in series in a circuit, what can we say about how the emf is shared between them?

Answer 4

The two components will be of identical resistance. This means that the total sum of the electromotive force in the circuit will be shared equally between the two components.

Question 5

If a (parallel) circuit has more than one branch/loop, what can we say about the potential difference in the circuit?

Answer 5

The potential difference in each ‘loop’ is equal to the electromotive force, and is independent of that of the other loop. This means that whatever components we add to one branch does not affect the voltages within the other branch.

Question 6

Describe the trend with resistors added in series. Include an equation.

Answer 6

R(total)=R1+R2+R3…+Rn
Essentially the total resistance R in a closed loop of a series circuit is equal to the sum of the resistances of components connected to it, since each added resistor effectively ‘increases the length’ of the singular path of the charges.

Question 7

Describe the word with resisters added in parallel. Include an equation.

Answer 7

1/R= 1/R1+1/R2…+1/Rn
Essentially each resistor we add provider another ‘path’ for current to take. This effectively reduces the cross-sectional area, reducing overall resistance as more resistors are added in succession.

Question 8

Why do car batteries have a very low internal resistance?

Answer 8

This is to enable them to supply the very high currents required to operate the starter motor of a car.

Question 9

Why do lost volts occur at the power source, giving rise to a lower terminal p.d.?

Answer 9

• The charges do work as they move through the power sources, due to reactions between the chemicals or resistance in the materials of the cell.
• This means that not all of the electromotive force (energy transferred) is available to the rest of the circuit.
• This means that terminal p.d. is less than the original emf.

Question 10

What equation links emf, terminal p.d. and lost volts?

Answer 10

Electromotive force = terminal p.d. + lost volts

Question 11

How does terminal p.d. differ from electromotive force?

Answer 11

Electromotive force does not consider the lost volts arising due to the internal resistance of the power supply. Terminal p.d. instead is measured from the termini of the power source, and describes how much of the total emf is available for the rest of the circuit to use.

Question 12

What happens to terminal p.d. and lost volts when the current increases.

Answer 12

• As current increases, more work is done per unit time by the charges passing through the power source.
• This means that the value of lost volts must increase by V=Ir.
• Since terminal p.d. = emf - lost volts, the terminal p.d. must decrease as a result.

Question 13

How do we calculate lost volts given the internal resistance of a power supply?

Answer 13

Lost volts (V) = current (I) * internal resistance (r)
- Here, note that internal resistance is denoted by a lower case ‘r’.

Question 14

What equations can we use to calculate the emf from a power source?

Answer 14

EMF = terminal p.d. + lost volts
Therefore - EMF = V+Ir, so EMF=IR+Ir
Taking out a factor of I - EMF=I(R+r)

Question 15

If a circuit diagram does not include terminal p.d., what should we assume in regards to this?

Answer 15

The power supply must be of negligible internal resistance, so we do not need to factor this into our calculations. Therefore, we can just use the simplified equation V=IR rather than emf=I(R+r).

Question 16

How could we practically investigate internal resistance? Describe a method.

Answer 16

• We could connect a voltmeter across a power supply (cell) and an amateur to the rest of the circuit in series with a variable resistor.
• We could record values of terminal p.d. by drawing varying values of current from the power supply.
• These results could then be plotted on a graph. Re-arranging emf=V+Ir we get V=-rI+emf, allowing us to extrapolate for the true emf of the cell and in turn the internal resistance which is the negative of the calculated gradient: -(-r) = r.

Question 17

Why must we ensure that current does not become too high when investigating internal resistance?

Answer 17

If current becomes too high, the temperature of the cell will increase, increasing the internal resistance above the constant that we expect. This is because the increased rate of flow of charge causes more work to be done per second by the charges flowing through the cell, increasing the loss of energy to thermal stores.

Question 18

How can a high internal resistance act as a safety measure?

Answer 18

A high internal resistance limits the current being supplied in high-voltage environments. This reduces the possibility of a fatal current being passed through someone if a fault develops.

Question 19

Why do mobile phone batteries often have a low internal resistance?

Answer 19

This enables a battery to be recharged using higher currents without the associated dissipation of energy to thermal stores, so more energy overall is transferred to the chemical stores in the battery. This reduces recharging time significantly.

Question 20

Should cells be connected in series or in parallel to maximise current?

Answer 20

• If we connected cells in series, the total emf would increase, but the increase in current would be inhibited by the internal resistance of the cells connected in series.
• However, the internal resistance is considerably smaller in parallel, whilst the supplied emf remains the same. This means that, overall, a greater current can be delivered in parallel.

Question 21

What does a potential divider circuit do?

Answer 21

These use fixed or variable resistors to alter the potential difference across an output from that of the input electromotive force.

Question 22

How does a potential divider circuit work?

Answer 22

• We know that the p.d. across each resistor in series depends on the ratio of total resistances, so if two resistors have the same resistance p.d. is shared equally for example as the ratio is 1:1.
• We can use this to provide our desired p.d. across a resistor, to which we can connect an output circuit in parallel with the same p.d. - since potential difference is equal in parallel loops.

Question 23

How can we express the ratio of resistances and their related potential differences algebraically?

Answer 23

V1/V2=R1/R2

Question 24

What is the potential divider equation?

Answer 24

V(out)=V(in)*R2/(R1+R2…)

Question 25

Explain the effect of loading a potential divider.

Answer 25

• Loading a potential divider is when we connect a component or circuit to our V(out) in parallel with the related resistor.
• As we know, adding resistors in parallel decreases the total R(combination). This alters the ratio of resistances, such that the loaded combination receives a lower proportion of the total emf. Therefore, V(out) and therefore the new V(load) must be reduced.
• The ‘resistors in parallel’ equation implies that adding a high load resistance has little effect on V(load), whereas a small resistance hugely impacts V(load).

Question 26

If we want to maximise V(load) when loading a potential divider, should the load be of high or low resistance?

Answer 26

The load circuit should be of high resistance. This is because adding a resistor of high resistance in parallel has little effect on R(combination) so the ratio of potential differences is largely unaffected.

Question 27

How do sensing circuits produce a varying V(out)?

Answer 27

• One of the resistors in series, from which V(out) is tapped off, should be replaced with a component whose resistance can change. This could be a variable resistor, LDR, thermistor, etc.
• This will therefore enable the operator or an external factor to modify the ratio of resistances.
• This will in turn enable V(out) to vary as resistance changes.

Question 28

How might we produce a light sensor using sensing circuits?

Answer 28

We could produce a series circuit containing an LDR and a fixed resistor. A load component could be connected to V(out) in parallel with the fixed resistor. As light intensity increases, the resistance of the LDR decreases, so the fixed resistor receives a greater proportion of the total EMF, so V(out) increases providing a current sufficient to activate the loaded component.

Question 29

How do potentiometers work?

Answer 29

A potentiometer has 3 terminals - input A, output B and a sliding contact.
- When the contact slides towards A, V(out) increases since the resistance between the contact and B (across which V(out) is connected in parallel) is higher.
- When the contact moves towards B, V(out) decreases until it reaches zero when it reaches B, for the same reason.

Question 30

Why might a potentiometer be more useful than a potential divider in some circumstances?

Answer 30

Potentiometers can be made considerably more compact than potential dividers, so are useful in small devices like mobile phones. They can be constructed to provide linear of logarithmic changes in V(out), and can be manufactured in different form factors such as dials or sliders.