When a thermistor is connected in series with a fixed resistor, how to explain the p.d. varies as resistance temperature changes?

When two components are connected in series, where one is a fixed resistor and the resistance of the other can vary (e.g. thermistor, light dependent diode, variable resistor etc), you always make use of the fixed resistor to explain the its p.d. as resistance is constant.

Then use the concept of sum of p.d. across both components is equal to the e.m.f of the circuit to explain how the p.d. across the other component varies.

Though thermistor is not in SciPhy syllabus, it can still be tested as long as the information on thermistor is given. Refer to the videos below where 2 are from Sciphy and the other is from Pure.

SP2020Q9

SP2013Q11

PP2008Q11OR

Using P = I^2R and P = V^2/R to explain which component uses the highest power or energy.

Instead of P = IV to explain, it might be easier to explain using P = I^2R when the components are connected in series where current I is constant. Hence power P is directly proportional to R. The bigger the R, the more power it uses.

Likewise, if the components are connected in parallel, it will be easier to use P = V^2/R, as the potential difference is constant for the components connected in parallel. Hence, power P is inversely proportional to R. The smaller the R, the more power it uses.

SP2021Q8

PP2017Q11

Finding Total Effective Resistance

Am I paying a lot on electrical bill for charging my phone?

With new advances in mobile devices, the battery capacity of the lithium-ion battery increases with each new model.

For instance, the flagships phone like iPhone 14 max Pro has an capacity of 4323 mAh, Samsung S22 Ultra 4855 mAh and the Z fold 4 4400 mAh. We tend to think that the constant charging of our phones will use a lot electrical energy, hence increases our electrical bill.

But is it true?

Diodes and bulbs, which bulbs is lighted up when switch S is open and closed

Answer: Option B

DC Question – Find unknown R, given the voltmeter readings when switch P and Q are closed respectively

Answer: Option A

1st Electricity Experiment

Below is a simple electrical experiment to determine the resistance of the unknown resistor. Take some time to look through these series of video to have a better understanding on how to do the connection and taking readings from the instruments.

Refer to this blog post for better understanding of the experiment and some information on ohmic conductor.

Finding unknown resistor R and setting up the electrical circuit

Basic set up

If Connections of Ammeter/Voltmeter are swopped

Different types of connecting wires

Connecting Variable Resistor

How To Read An Ammeter

How to Read A Voltmeter

Basic Concepts on DC Circuit – river system

The ‘D.C.’ here mean direct current. It means that the current flows in one direction in the circuit.

The direction of the direct current refers to the conventional current, and it flows out of the positive (+) terminal of the cell / battery, around the circuit and flows back into the negative (-) terminal.

[Note: the direction of the electron flow is opposite to the conventional current]

To understand DC circuit, it will be useful to relate to a river system. Refer to the 3 videos below to learn more about 01: DC circuit similar to river system, 02: Series Circuit 03: Parallel Circuit and 04: Combined Circuit.

01: How is DC circuit related to a river system

02: Series Circuit

03: Parallel Circuit

04: Combined Circuit (Series and Parallel)

Now, after you have the basic concepts and rules for the circuits, let’s look at some simple example to reinforce you understanding.

Example 01: Series Circuit

Example 02: Parallel Circuit

Example 03: Combined Circuit

Example 04: PP2012P2Q7 DC circuit : pd across 2 points on two separate branches.

Hope these series of videos help in you understanding of DC circuit.

DC Circuit is just like a River System!

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Simple electric circuit set up

This simple circuit involves a resistance wire on the meter rule and the use of jockey tapping at different length L on the resistance wire.

Note that this is not a potential divider. Rather this set up works like a variable resistor (rheostat) in the circuit. When the switch is closed (jockey NOT tapping on resistance wire), there is no current flowing as voltmeter (infinity resistance) is connected in series with the ammeter and the battery. Hence the voltmeter is showing the battery’s electromotive force (emf) of 3.0 V.

When the switch is closed and the jockey is tapped on the resistance wire on the ruler, the longer the L (length of resistance wire), the higher the resistance of the circuit, the higher the potential difference (voltmeter) across the resistance wire and the smaller the current through the ammeter. Hence the tapping of the jockey on the resistance wire is similar to adjusting the resistance on the variable resistor.

(If you are wondering why the voltmeter is not showing the emf of the battery when the jockey touches the resistance wire L, it is because in reality there is internal resistance in the battery or even in the connecting copper wire. For olevel theory we assume no internal battery resistance or resistance in copper wire or ammeter).

To learn how to set up the experiment, refer to the video below.

Both ammeter and voltmeter have two terminals, (positive and negative). The conventional current must flow into the positive terminal (+) of the meters and out of the negative terminal (-).  If the connection is the opposite, the needle will deflect below the zero marking. Refer to the video below.

Sometimes, the connection terminals on the voltmeter and ammeter are different. Likewise, different types of wire with different connection heads have to be used. Refer to the video to see how are they connected in general.

Click here for another set up of a simple electrical circuit to determine the unknown resistor.

 

2016 Pure Physics P1 Q40 – Voltage and Power of Bulb Y when X is switched off

Solutions: Option C
[There is another similar question in 2013 Nov Pure Physics P1Q40. The answer is Option C too. Refer to the last section of this post]

Refer to the 2 videos below. The 1st one is faster if you know that the bigger the resistance, by proportion, the bigger the potential difference of the component as it will take a larger portion of the emf wrt to the other components in series. This method is especially useful for MCQ.

If you are still unsure, you may put in values to find the I, V and P across the components. This will be more tedious and time-consuming.

Another similar question is 2013 Nov Pure Physics P1 Q40.

Solutions: Option C

Cells in parallel vs single cell

Answer: Option C

Common Electrical Symbols

These are some of the necessary electrical symbols that you must know. Those in grey background are for Pure Physics.

Finding total effective resistance

Potential Divider Summary

2013SPp1q17 What is the new P when V across resistor is doubled?

Solutions: C

Alternatively, you may put values to work out using the 2 basic formulae of P = IV and V = IR. Refer the video below.

Why lighting circuit should be connected in parallel?

Lighting circuit, in fact all circuits at home, should be connected in parallel.

Reasons being:
When one bulb is spoilt or switched off, the rest of the bulbs can still function normally at normal brightness. This is because the potential difference across each bulb in the branches remains the same.

Refer to series and parallel circuits summary.

If the lighting circuit is connected in series, when one bulb is spoilt or switched off, it will be an open circuit and no current can flow through the circuit. Hence all the bulbs cannot function.

Refer this post for the concept of earth wire and the fuse

Rules of Series and Parallel Circuits

Rules of Series and Parallel Circuits

To understand direct current (DC) circuits, the best way is to think in terms of river system.

Series Circuit

Parallel Circuit

Series and Parallel Circuit

 

Examples:

Finding effective resistance when a wire is bent into different shapes

The concepts needed to solve such questions

1. Length increases, resistance increases and vice versa.
2. Finding resistors in parallel and in series.

N2010 P2Q12 Fuel gauge using variable resistor

Solutions:

View the video on how the gauge works.

As the fuel level drops, the float which stays on the fuel surface will descend. The rod which is attached to the float will turn clockwise about the pivot X. As the rod turns, the resistance on the variable resistor increases. This increases the resistance of the circuit. Hence the current flowing through the circuit will decreases, causing the needle to deflect more to the left, indicating towards E (empty). Thus the reading on the fuel gauge decreases.

Solutions:

(i) Both the fixed resistor and sensor are in series.

Total effective resistance Re = 5000 + 1000 = 6000 ohms

V = IR
12 = I x 6000
I = 0.0020 A

Hence potential across Y, V = IR (where I is constant in a series circuit)
= 0.0020 x 1000
= 2.0 V

(ii) When the temperature increases and the resistance of sensor Y decreases, the total effective resistance of the circuit decreases. Current flowing through the circuit increases.

Since V = IR, where the R of the fixed resistor is a constant 5000 ohms, as current I increases, the potential difference across the 5000 ohms resistor will increase.

Physics Meditation – Enlightenment

FLHR

Solutions: Option D

DC Circuit Calculations

Solutions: Option A

Electric Circuit vs River Flow

Series and Parallel Circuit

Brightness of bulb as resistance of rheostat increases

Solution:A

As resistance of the rheostat increases, the total resistance in parallel will increase. Hence potential difference across the parallel bulb Q increases, therefore BRIGHTER.

Total effective resistance of the circuit (include resistance of bulb P) increases, main current thought circuit (bulb P) decreases. Hence bulb P DIMMER.

You can think in terms of p.d of bulb P. Since p.d. across parallel branches increases, p.d across bulb P decreases, hence bulb P is DIMMER.

Without calculation, using resistance and p.d. is easier. To convince yourself, refer to the following diagrams with imaginary numbers.

The 5 Formulae for Electricity

Sent from my iPad

DC Circuit – Diode

An a.c. circuit is shown below.

Which of the following diagrams show the voltage V across the resistor?

 

Solutions: Option C

The power supply is a alternating supply, hence direction of current changes many times in 1 second. (alternating current = a.c.)

You may ask which direction of current should you first assume in order to represent the first ‘hump’?

That is not that important. Rather you must be able to know that the ‘humps’ should alternate as the V across alternates due to the diodes.

When current flows in anticlockwise, current will flow through the 6Ω and the 12Ω (in series). When the current flows in clockwise, current will flow through the 12Ω and the 12Ω (in series). Hence V across the 6Ω and the 12Ω will alternate. Hence B and D are out.

D is out as there is an continuous alternating current flowing through the circuit. Not rectification due to the diodes in the circuit.

The diodes in the 2 branches only stop current from flowing in either branch at any one time, current still continue to flow through the circuit.

Consider when current flows anticlockwise, the V is across the 6Ω. As 6Ω is smaller than the 12Ω in series, the p.d. across 6Ω is smaller. Hence a smaller ‘hump’.

On the other hand, when current flows clockwise, the V is across the 12Ω. As this 12Ω is equal to the 12Ω in series, the p.d. across will be higher than across 6Ω previously. Hence bigger ‘hump’. So C is the answer.

Drawing Voltage-Position Graph for a circuit

How to draw the voltage-position graph for the circuit.

Basic concepts:

– Electromotive force (emf) is the work done in bringing a unit charge across the whole circuit.

– Potential difference (p.d.) is the work done in bringing a unit charge across the conductor (e.g resistor, bulb)

– Sum of potential differences across the conductors in a series circuit is equal to the emf of the battery.

You can assume there is no potential drop between 2 points on a wire.