3.2 - Complete Electrical Cicuits

Question 1

What are 2 of the fundamental rules governing measurements in electrical circuits

Answer 1

The conservation of charge and conservation of energy - these determine how current, voltages and resistances change around any particular circuit

Question 2

Tell me about the total amount of charge in a circuit

Answer 2

The total amount of charge within a circuit cannot increase or decrease when the circuit is functioning.

Question 3

Where must current be measured

Answer 3

Currents are measures of charge flow through a component, so they must be measured in the same line as the component eg ammeter must always be placed in series next to component

Question 4

Does an ammeter have high or low resistance

Answer 4

must have very low resistance to avoid significant alteration of the current it is to measure - resistance of ammeter can’t affect reading

Question 5

What’s current like In series circuits

Answer 5

Any group of components that follow in series in a circuit, with no junctions in the circuit, must have the same current through them all

Question 6

What’s current like in parallel

Answer 6

Whenever a current goes through a junction in a circuit, the charges can only go one way or the other, so current must split.

The proportions that travel along each possible path will be in inverse proportion to the resistance along that path - if path has high resistance, current less likely to go that way

But the total along the branches must add up to the original total current in order to conserve charge

Question 7

How are voltages measured in circuits

Answer 7

Voltmeters must always be in parallel across the component they are measuring

Voltages are measures of energy change as charge passes through a component, so they must be measured from one side to the other so it is placed in parallel across the component

Question 8

Why do voltmeters have high resistance

Answer 8

A voltmeter measures the voltage difference between two different points of a component but it should not change the amount of current going through the element between those two points. So, it should have very high resistance so that it doesn’t “draw” current through it.

Question 9

What is voltage like in series circuits

Answer 9

Any group of emfs that follow in series in a circuit, with no junctions in the circuit, will have a total emf that is the sum of their individual values, accounting for the direction of their positive and negative sides

Eg two 1.5v bells in series will supply an emf of 3 V

Take account for their directions, as cells in opposite directions oppose eachother and cancel out the emf they would supply

Question 10

What are voltages in parallel circuits like

Answer 10

If the voltage across any branch of a circuit is know then the voltage across any other branch in parallel with it will be identical

Eg a voltmeter read 6V on one branch so the voltage is the same acros all parallel branches within a circuit

Question 11

How is resistance found / measured

Answer 11

Resistance can be calculate from ohms lass as V/I - this can be done for any individual component or a whole branch of a circuit as long as current and voltage is known

Question 12

What’s resistance in series like

Answer 12

Any group of resistances that follow in series in a circuit, with no junctions in the circuit, will have a total resistance that is the sum of their individual values

Total R = total V / I

R total = R1 + R2 + …

Question 13

Should be account for resistance of ammeter and voltmeter

Answer 13

Ammeters in series and voltmeters in parallel do not affect the total resistance and so can be ignored

Question 14

How do we do the derivation of Rtotal = R1 + R2 + R3

Derive resistance in series

Answer 14

Resistors in series will have a total pd across them that is the sum of their individual pds

Current through them will be the same for each one so

Vtotal = V1 + V2 + V3

V = IR
IRtotal = IR1 + IR2 + IR3 

Since I is the same
It becomes Rtotal = R1 + R2 + R3

Question 15

What is resistance like in parallel

Answer 15

the total resistance of a group of resistors in parallel can be calculated from the equation

1/Rtotal = 1/R1 + 1/R2 + 1/R3

Resistors in parallel follow a reciprocal sum rule to find their total resistance

Any combination of resistors in parallel will have a total resistance that is smaller than the smallest individual resistance in the group

Question 16

How do we derive the rule of resistors in parallel

Answer 16

Resistors In parallel will have a total current through them that is the sum of their individual currents in branches. The pd across them will be the same for each branch

Itotal = I1 + I2 + I3

I= v / R

V/Rtotal = V/R1 + V/R2 + V/R3

Therefore
1/Rtotal = 1/R1 + 1/R2 + 1/R3

Question 17

How do we find resistance when resistors are in branch combinations

Answer 17

If a circuit has a mixture of series and parallel combinations, we must use the rules we have for each group of resistors and then use the rules again to combine these sub-totals

Calculate total resistance of resistor groups separately, before using the appropriate rule to combine the sub totals together

Question 18

How can we investigate circuit rules (practical)

Answer 18

Make a complex circuit with various components in series and parallel combinations

Using only ammeter and voltmeter, your partner should be able to verify the circuit rebukes explained in this sections - if the resistances are large, ammeter may need to be a multimeter set to read milliamperes currents

Join various resistors in various combinations of series and parallel connections. Your partner should be able to calculate what they expect the overall resistance of the combination to be - check wether they are right by measuring overall resistance of the resistor combination using an ohm meter

Question 19

Who was Gustav Kirchoff

Answer 19

A physicist who presented the conservation of charge and of electrical energy within a circuit as 2 laws of physics

Question 20

What’s the electric current rule

Answer 20

Electric current rule: the algebraic sum of the currents entering a junction is equal to zero

Weird E (symbol for the sum of) I (current) = 0
EI = 0

In order to conserve electric charge, the sum of all the currents arriving at any point (such as a junction) in a circuit is equal to the sum of all the currents leaving that point.

Question 21

Tell me about the electric voltages rule

Answer 21

In order to conserve electrical energy around any closed loop in a circuit, the sum of the emfs is equal to the sum of the pds around that loop - loop must be complete

If current flowing the same direction as components and cell - voltages all in the same direction 
So Ee(e for emf) = EV

If there is no Emfs (supply voltages) then look at directions of closed loop and Ee = 0 therefore Ev = 0

Question 22

Tell me about voltages rule with calculated pds

Answer 22

Potential differences are the product of currents passing through resistances, in order to use up electrical energy. Thus, each pd can be calculated from Ohms law as V = IR

So Ee = EIR

Question 23

What’s the electric current rule

Answer 23

The algebraic sum of the currents entering a junction is equal to zero

EI = 0

Question 24

What’s the voltages circuit rule

Answer 24

Around a closed loop, the algebraic sum of the emfs is equal to algebraic sum of the pds

Ee = EIR

Question 25

How does voltage split up in s circuit

Answer 25

We have seen that all the voltage supplied by emfs in a circuit loop must be used by components as potential differences at other points around the circuit loop

The way that the voltage splits up is in propotion to the resistance of the components in the circuit loop

Question 26

Tell me an example of a potential divider circuit

Answer 26

The voltages across 2 resistors must add up to 6V (supply), the 20 ohm resistor has twice the resistance so takes twice the voltage of the 10ohm resistor - this is a potential divider circuit

Question 27

How does ohms law explain why the voltage is split in proportion to the resistance

Answer 27

Consider 2 resistors with residences R1 and R2, and their corresponding voltages (V1 and V2)
- calculating the current through each one gives

I1 = V1/R1 and I2 = V2/R2

But they both have the same current through them so I1 = I2 therefore

V1/R1 = V2/R2
Therefore

V1/V2 = R1/R2

Question 28

What does V1/V2 = R1/R2 tell us

Answer 28

So the voltage is split in the same proportion as the ratio of the resistance for any Values of resistance

This means that for a known emf supply voltage, we can use Carefully chosen resistances to share the voltage and provide a specific value of pd on one component

If we then also remember that all parallel branches in a circuit must have the same voltage, then any branch we set up in parallel with that specific pd will also have the same voltage, thus we can set up a circuit to provide an exaclty chosen value of voltage to the parallel branch

Using variable resistors, this set up can then be used to prove whatever voltage we choose - particularly useful if emf is a fixed value like a battery

Question 29

What happens when we adjust a variable resistor

Answer 29

Adjusting the variable resistor alters the proportion of the voltage it takes, and so the pd that is left for the resistance wire /(any other component - resistance wire just an example)can be varied to any value we choose

If variable resistor set to high resistance, it will have high pd and so only a little bit for the redtisnce wire (or any other components that are there)

Question 30

How do we use a potential divider circuit to make an IV graph

Answer 30

By changing the resistance of the variable resistor, the pd across the component being measured will change - we can adjust variable resistor to a set of value of pd on the component to those we need of I-V graph plot

Question 31

Tell me about the potential divider equation

Answer 31

As the pd in a potential divider circuit is split in proportion to the resistances of the components, we can calculate the pd across them mathematically

Vout is the thing we want to calcaulte and v In is the supply voltage

R2 is usually the restisnce of the component we want

Vout = Vin x (R2/R1 + R2)