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School-college Physics Notes: Electricity 3.6 E = QV calculations

Electricity Section 3: 3.6 How are potential difference (V), quantity of charge (Q) and energy transfer (E) related? E = QV calculations

[Author © Dr WP Brown PhD: Doc Brown's physics exam revision notes suitable for students of UK IGCSE & GCSE level physics courses, ~ US grades 9-10 physics, electricity page updated Feb 8th 2026]

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INDEX for electricity section 3 notes on current, voltage, resistance, energy & charge transfer in circuits

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3.6 Potential difference and energy transfer

Introduction to calculating electrical energy transferred

Energy transfer per unit of charge = potential difference (p.d.) and calculations based on E = QV

In the previous section we looked at how to calculate the quantity of charge moving in a circuit, but said nothing about the energy transferred.

Reminders:

Electrical circuits, terms used, circuit symbols, parallel circuits and series circuits explained

Potential difference (p.d. in volts, V) is the energy transferred per unit charge as electric charge moves from one point to another in an electric circuit.

It is measured with a voltmeter, which is always wired in parallel across a circuit component.

An electrical current transfers energy

Just think of all the electrical appliances you use - all need supplying with energy to work!

A power supply does work on a charge and transfers energy to it.

Work must be done on the charge to increase its potential energy.

Electric charge is measured in coulombs (C)

Charge and its movement has already been dealt with in Part  3.5 (Q = It)

Charges transfer energy to components as they pass through by doing work against the resistance of the component.

If work is done, then energy is transferred.

 

If electrical charge experience a potential difference, that charge will flow transferring energy.

The energy is supplied from the energy store of the power supply - battery, mains electricity etc.

When charge passes through any p.d. fall it releases energy (from a higher to a lower potential energy level).

e.g. in a thin wire resistance, thermal (heat) energy is released, AND,

the potential difference between two points is equal to the work done per unit charge.

potential difference (V) = work done (energy transferred in J) ÷ charge (C)

i.e. 1 volt corresponds to 1 joule per coulomb  or  V = J/C

The bigger the fall in p.d., the greater the energy transferred, because the charge starts off with a greater potential energy.

Therefore a power supply with a bigger source p.d. (V) can supply more energy to the circuit per unit of electric charge (the coulomb, C).

The bigger the p.d., the more energy the same quantity of electric charge can carry.

 

 Another equation to calculate electrical energy transfers

The quantity of energy carried can be calculated from the equation:

energy transferred = charge x potential difference.

E = QV,  so  Q = E/V  and  V = E/Q,

(learn to rearrange, its better than using the formula triangle)

E = energy transferred in joules (J)

Q = quantity of electric charge in coulombs (C)

V = potential difference in volts (V)

Noting that: V = E/Q = energy transferred per unit charge (J/C)

 

Just in passing and some reminders:

The more energy transferred in a given time, the greater the power of a device or electrical appliance.

The p.d. V tells you how much energy each unit of electrical charge transfers,

so,  V = E/Q, (units J/C), see  E = QV calculations below).

The current I tells you how much charge passes a given point in a circuit per unit time (coulombs/second, C/s).

This means both p.d. V and current I affect the rate at which energy is transferred to an appliance from the electrical energy store to other energy stores.

AND some mathematical connections based on section 2. Q = It and here in section 3 E = QV

From Q = It and E = QV, substituting gives E = ItV,

so (i) E = IVt (I in A, t in s, V in volts)

Rearranging E = IVt gives IV = E/t

This connects with the equations for power

(ii) Power = energy transferred / time taken = E/t (J/s),  and

(iii) Power = current x voltage = P (W) =  I (A) x V (V), P = IV

From (ii) and (iii) E/t = IV, so E = IVt, which is equation (i) !!!

Calculation questions based on E = QV

(sometimes involving other electricity equations too)

Q1 An electric motor of a model car is powered by a 1.5 V battery.

If 120 C of charge passes through the motor circuit in the moving car,

(a) how much energy is transferred?

(b) Describe the likely energy store changes when the car is running.

ANSWERS

 

Q2 What quantity of charge is needed to transfer 500 J of energy if the p.d. of a circuit is 24.0 V?

ANSWERS

 

Q3 What potential difference is required in a circuit to transfer 2000 J of energy with a charge of 50 coulombs?

ANSWERS

 

Q4 A 12.0 V battery passes a current of 2.0 A through a lamp for 5 minutes.

(a) Calculate how much charge passed through the lamp.

(b) Calculate how much electrical energy was transferred by the lamp.

ANSWERS

 

Q5 An appliance has a power of 1.5 kW and works of a 230 V mains supply.

If the appliance is used for 15 minutes, how much charge has flowed through the circuit?

ANSWERS

 

INDEX of electricity section 3 notes on current, voltage, resistance, energy & charge transfer in circuits including Ohm's Law investigations

Key points about electric circuits in physics courses - p.d. voltage and energy transferred

Information sources for Doc Brown's key points: IGCSE-GCSE physics are based on textbooks & syllabus-specifications for students taking the UK AQA, Edexcel, OCR 21st Century Science, OCR Gateway science suite, WJEC, CCEA and CIE GCSE physics 9-1 level science examinations.

Keywords, phrases and learning objectives for calculations in electricity involving charge, time, current, power and energy

Know how are potential difference, energy transfer and electric charge relate to each other

Be able to do calculations involving the equation relating energy transferred, potential difference and the quantity of electric charge transferred.

Be able to rearrange and use the following equations E = QV Q = E/V V = E/Q in calculations e.g. use in problem solving on energy J transferred given p.d. voltage V and charge in coulombs C.

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ANSWERS to calculation questions based on E = QV

Q1 An electric motor of a model car is powered by a 1.5 V battery.

If 120 C of charge passes through the motor circuit in the moving car,

(a) how much energy is transferred?

E = QV  =  120 x 1.5 = 180 J

(b) Describe the likely energy store changes when the car is running.

The chemical potential energy store of the battery decreases and becoming electrical energy.

The kinetic energy store of the car increases with some wasted heat from friction and sound energy transferred to the thermal energy store of the surroundings.

 

Q2 What quantity of charge is needed to transfer 500 J of energy if the p.d. of a circuit is 24.0 V?

E = QV,  Q = E/V  =  500/24 = 20.8 C (3 sf)

 

Q3 What potential difference is required in a circuit to transfer 2000 J of energy with a charge of 50 coulombs?

E = QV,  V = E/Q = 2000/50 = 40 V

 

Q4 A 12.0 V battery passes a current of 2.0 A through a lamp for 5 minutes.

(a) Calculate how much charge passed through the lamp.

Q = It = 2 x 5 x 60 = 600 C

(b) Calculate how much electrical energy was transferred by the lamp.

Two ways:

(i) E = QV = 600 x 12 = 7200 J

the simplest, but you can calculate it without knowing Q from:

(ii) E = IVt = 2 x 12 x 5 x 60 = 7200 J

 

Q5 An appliance has a power of 1.5 kW and works of a 230 V mains supply.

If the appliance is used for 15 minutes, how much charge has flowed through the circuit?

1.5 kW ≡ 1500 W ≡ 1500 J/s

Total energy transferred = power x time = 1500 x 15 x 60 = 1 350 000 J

E = QV,  so Q = E / V = 1 350 000 / 230 = 5870 C (3 sf)

The answer can be calculated by another route

P = IV,  I = P / V = 1500 / 230 = 6.522 A

Q = It = 6.522 x 15 x 60 = 5870 C (3 sf)

 

INDEX of electricity section 3 notes on current, voltage, resistance, energy & charge transfer in circuits including Ohm's Law investigations

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