GCSE Physics Equations Sheet

This blog will prepare you for the upcoming Physics exams, recapping all the equations you will need when to use them.

As a bonus, we’ve crammed them all into an easy-to-use formula sheet you can download here. That way, you can practice your past papers without being tempted to look in the book for answers!

From Energy and Electricity to Forces, Waves, and Magnetism, we'll break down each unit, providing a short description and example questions to reinforce your understanding.

Say goodbye to exam jitters and hello to success in Physics – let's jump in!

Unit 1: Energy

These formulas serve as the foundation for our knowledge of energy stores and transfers, from calculating exactly the amount of energy stored and transferred, to understanding the efficiency of energy transformations.

1. Kinetic Energy ( K.E) 

Energy stored in the Kinetic energy store of a moving object with a mass ‘m’ and speed ‘v’ is given by the equation,

Example Question: A bicycle with a mass of 10 kg is travelling at a speed of 5 m/s. Calculate its energy stored in the kinetic energy store.

To find the speed of the object, given the mass and kinetic energy:

Example Question: A car with a mass of 1000 kg has a kinetic energy of 250,000 J. Determine the speed of the car.                  

2. Gravitational Potential Energy (G.P.E)

The energy stored in the gravitational potential energy store of an object with a mass ‘m’ and placed at a height ‘h’ is given by the equation,

Example Question: A book with a mass of 2 kg is placed on a shelf 5 metres above the ground. Calculate its gravitational potential energy relative to the ground.

3. Power and Energy transferred

Power is the rate of energy transferred, or the rate of work done.

And always remember, Work done is the same as energy transferred.

Example Question: A microwave oven consumes 1200 W of power to heat food. If it operates for 5 minutes continuously, calculate the total energy transferred to the food during this time.

(Remember to convert all the units to S.I units before doing the calculations!)

4. Efficiency

Efficiency of a device can be given by the equation,

Example Question: A light bulb consumes 60 J of electrical energy per second and emits 15 J of light energy per second. Calculate the efficiency of the light bulb.

Here, the total energy input will be the electrical energy consumed, which is 60 J, and useful output energy will be the light energy emitted, which is 15 J.

5. Elastic Potential Energy

The energy stored in a spring with spring constant ‘k’, while making an extension/compression ‘e’, can be given by the equation, 

Example Question: A spring with a spring constant of 200 N/m is compressed by 0.05 metres. Calculate the elastic potential energy stored in the spring.

Here, the extension will be 0.05 m.

Unit 2: Electricity

This unit mainly revolves around a charge Q, the Electric current I, the potential difference V and the resistance R. To answer a problem, you are likely to use multiple equations that are related to one another.

1. Charge Flow and Electric current:

The electric current I produced when a charge Q moves for a time t, is given as,

Similarly, the charge flow can be shown as,

2. Potential Difference, Electric current and Resistance:

The potential difference V, the electric current I, and the resistance R of a current-carrying conductor can be given as ,

Alternatively, the current and the resistance can be expressed as,

Now let’s look into a sample question involving these equations:

Example Question: In an electrical circuit, a battery with a voltage of 12 volts is connected to a resistor. If a total charge of 5 Coulomb flows through the circuit in 10 seconds, calculate the resistance of the resistor.

To find the resistance, first we have to find the current using the equation, I=Q/t

And then use the value of I to find resistance using the equation R=V/I

3. Total Resistance in Circuits:

The total resistance of a series circuit with components having individual resistances R1 and R2 can be given as,

Total resistance in series = resistance of component 1 + resistance of component 2.

Example Question: In a series circuit, resistor 1 has a resistance of 20 ohms, and resistor 2 has a resistance of 30 ohms. Calculate the total resistance of the circuit.

The total resistance of a circuit with parallel resistor components having individual resistances R1 and R2 can be given as,

The reciprocal of the total resistance in series = the reciprocal of the resistance of component 1 + the reciprocal of the resistance of component 2.

Example Question: In a parallel circuit, resistor 1 has a resistance of 30 ohms, and resistor 2 has a resistance of 60 ohms. Calculate the total resistance of the circuit.

(remember to convert the result of 1/R to just R!)

4. Power :

Power of an electrical component with resistance R, supplied with a potential difference V and a current I flowing through it can be given as,

Example Question: A circuit has a current of 2 A flowing through a resistor with a potential difference of 12 V across it. Calculate the power dissipated by the resistor.

Example Question: In a circuit, a resistor with a resistance of 5 ohms carries a current of 3 A. Calculate the power dissipated by the resistor.

5. Energy Transferred and Power:

Example Question: If a circuit with a power of 50 W operates for 2 hours, calculate the total energy transferred during this time.

(Time in hours should be converted to seconds before the calculation)

6. Energy Transferred and Electric charge:

Energy transferred by an electric charge Q at a potential difference V can be defined as,

Example Question: A battery with a potential difference of 6 V is used to charge a device, transferring a total charge of 500 C. Calculate the total energy transferred by the battery.

Unit 3: Particle Model of Matter

The Particle Model of Matter explores the behaviour of matter at the atomic level, providing insights into its properties, phase transformations and temperature changes.

1. Density:

Density of an object with mass ‘m’ and volume ‘V’ can be expressed as,

Example Question: A block of wood has a mass of 500 g and occupies a volume of 250 cm³. Calculate the density of the wood.

2. Change in Thermal Energy:

Change in thermal energy of a substance ‘Q' with mass ‘m’, specific heat capacity ‘c’, and a temperature change of can be given by the equation,

Example Question: A piece of metal with a mass of 0.2 kg is heated from 20°C to 100°C. If the specific heat capacity of the metal is 500 J/kg°C, calculate the change in thermal energy.

Change in thermal energy 'Q' of a substance with mass ‘m’ and specific latent heat ‘L’, subjected to a phase change at constant temperature can be calculated by the equation,

Example Question: Calculate the amount of thermal energy required to change 0.5 kg of ice at 0°C into water at 0°C. Given the specific latent heat of fusion of ice is 334,000 J/kg.

3. Pressure and volume of a gas*:

At a constant temperature, pressure and volume of a gas can be given by the equation,

This indicates that, if a gas with pressure and volume P1, V1 is compressed, resulting in a new value for pressure and volume P2 and V2, 

Example Question: A certain amount of gas occupies a volume of 5 m³ at a pressure of 200 kPa. If the volume of the gas is compressed to 2 m³, calculate the new pressure assuming the temperature remains constant.

Unit 5: Forces

1. Weight:

Weight ‘W’ of an object with mass ‘m’ standing on a planet with gravitational field strength ‘g’ can be given as,

Example Question: Calculate the weight of an object with a mass of 50 kg on Earth, where the gravitational field strength is 9.8 N/kg.

2. Work Done:

Work done ‘W’ by a force ‘F’ to move an object to a distance ‘d’, along the direction of the force can be given as,

Example Question: A force of 20 N is applied to move an object a distance of 5 metres along the direction of the force. Calculate the work done.

3. Force acting on a spring:

Force applied on a spring with spring constant ‘k’ producing an extension ‘e’ can be given by.

The work done by the spring can be given by,

Example Question: A spring with a spring constant of 100 N/m is extended by 0.2 metres. Calculate the force exerted by the spring.

4. Moment:

The moment of a force can be defined as,

Example Question: A force of 30 N is applied at a distance of 0.5 metres from a pivot point. Calculate the moment of the force.

5. Pressure*: 

Pressure ‘P’ of a gas exerting a force ‘F’ on an area ‘A’ of a container can be expressed as,

Example Question: Calculate the pressure exerted by a force of 500 N acting perpendicular to a surface with an area of 0.5 m2.

Pressure due to a column of liquid with density ‘' and height ‘h’ can be given by,

Example Question: Calculate the pressure exerted by a column of liquid with a height of 2 m, density of 1000 kg/m3, and gravitational field strength of 9.8 N/kg.

6. Forces and Motion

The distance travelled ‘d’ by an object moving with a speed ‘v’ in time ‘t’ can be given by,

And,

Example Question: A car travels at a constant speed of 20 m/s for 10 s. Calculate the distance travelled by the car.

The acceleration ‘a’ of an object which had an initial speed ‘u’ and a final speed ‘v’ over a time interval ‘t’ can be given by,

Example Question: A car accelerates from 10 m/s to 30 m/s in 5 s. Calculate its acceleration.

*The distance travelled ‘s’ by an object which changed its speed from ‘u’ to ‘v’ having an acceleration ‘a’ can be found by,

Example Question: A car starts from rest and accelerates at a rate of 2 m/s2 uniformly to a final speed of 20 m/s.Calculate the distance travelled by the car.

7. Resultant Force:

Resultant force ‘F’ acting on an object with mass ‘m’ causing an acceleration ‘a’ can be described as,

Example Question: A force of 50 N acts on an object with a mass of 10 kg. Calculate the acceleration of the object.

8. Momentum:

Momentum ‘p’ of a moving object with mass ‘m’ and speed ‘v’ can be defined as,

Example Question: Calculate the momentum of a ball with a mass of 0.2 kg moving at a velocity of 5 m/s

9. Force and Momentum*:

The relation between force ‘F’ and the change in momentum P over a time interval ‘t’ can be given as,

Example Question: A force acts on an object for 5 s, causing a change in momentum of 200 kg m/s. Calculate the force.

Unit 6 : Waves

1. Wave Speed:

The speed 'v' of a wave with wavelength ‘' and frequency ‘f’ can be calculated using the formula:

Example Question: A wave has a frequency of 50 Hz and a wavelength of 0.2 m. Calculate the wave speed.

2. Time Period:

The time period ‘T’ of a wave with frequency ‘f’ can be found using,

Example Question: Calculate the time period of a wave with a frequency of 20 Hz.

3. Magnification:

The magnification of an image can be determined using the formula,

 Example Question: An object is 5 cm tall and its image is 2 cm tall. Calculate the magnification of the image.

Unit 7: Magnetism and Electromagnetism

1. Force acting on a conductor in a Magnetic Field:

When a conductor of length 'l' carrying a current 'I', is placed in a magnetic field with flux density ‘B’, it experiences a force ‘F’ given by,

Example Question: A conductor carrying a current of 2 A is placed in a magnetic field with a magnetic flux density of 0.5 T and has a length of 0.1 m. Calculate the force acting on the conductor.

2. Transformer Equations*:

The ratio of the potential difference across the primary coil ‘Vp' and the secondary coil 'Vs' of a transformer with ‘Np 'number of coils in the primary and 'Ns' number of coils in the secondary can be given as,

Therefore, the potential difference across the secondary coil can be found by,

Example Question: A transformer has 100 turns in the primary coil and 500 turns in the secondary coil. If the potential difference across the primary coil is 50 V, calculate the potential difference across the secondary coil.

The ratio of potential difference and current across the primary (Vp, Ip) and secondary coils (Vs,Is) of a transformer can be given as,

Example Question: A transformer has a primary coil with 200 turns and a secondary coil with 400 turns. If the potential difference across the primary coil is 100 V and the current in the primary coil is 5 A, calculate the potential difference across the secondary coil when the current in the secondary coil is 2 A.

The current in the secondary coil can be found by rearranging the above equation,

*Fields marked are applicable for Separate Physics only (not combined science).

To sum up, mastering the equations covered in your GCSE Physics papers is an achievable feat with dedication and practice. Remember, understanding the principles behind each equation is just as important as memorising them.

As you prepare for your exams, don't hesitate to reach out to your teachers or peers if you encounter any challenges. You may wish to enlist the help of a GCSE Physics tutor. Keep practising example questions, reviewing concepts, and applying these equations to real-world scenarios.

With persistence and a solid grasp of these equations, you'll be well-prepared to tackle your Physics exams with confidence. Best of luck on your academic journey, and may your efforts yield the success you deserve!