# Electrical Charge

## Key Stage 3

### Meaning

Charge is a property of matter that can cause an electrostatic force between two objects.

There are two types of charge; positive and negative.
Like charges repel each other and opposite charges attract each other.
Charges create an electrostatic field which affects other charged objects.

To see the electrostatic field created by a charge click on the picture below to play a PHET simulation.

## Key Stage 4

### Meaning

Charge is a property of matter that can cause an electrostatic force between two objects.

The SI Unit of charge is the Coulomb (C).
Charge is a scalar quantity as it has magnitude but does not have a direction.
There are two types of charge; positive and negative.
Like charges repel each other and opposite charges attract each other.
Charges create an electrostatic field which affects other charged objects.
Charge is a conserved quantity which means; "Charge cannot be created or destroyed, it can only be transferred from one place to another."
A flow of charge is an electrical current.

### Equation

#### Equation linking Charge, Current and Time

NB: You should remember this equation with charge as the subject of the formula.

Charge = (Current) x (time)

$$Q=It$$

Where

$$Q$$ = The amount of charge flowing past a point.

$$I$$ = The electrical current

$$t$$ = The time taken for the charge to flow.

#### Equation linking Charge, Potential Difference and Energy Transferred

NB: You should remember this equation with energy transferred as the subject of the formula.

Charge = (Energy Transferred)/(Potential Difference)

$$Q=\frac{E}{V}$$

Where

$$Q$$ = The amount of charge that moves between two points.

$$E$$ = The Energy Transferred by the charge.

$$V$$ = The potential difference between two points.

### Example Calculations

#### Finding Current from Charge and Time

 A charge of 15 Coulombs passes through a point in a circuit ever 0.52 seconds. Calculate the current flowing past this point correct to two significant figures. A capacitor stores a charge of 10C. It discharges in 12ms. Calculate the average current flowing out of the capacitor correct to two significant figures. 1. State the known quantities in correct units. Q = 15C t = 0.52s 1. State the known quantities in correct units. Q = 10C t = 12ms = 12x10-3s 2. Substitute the numbers and evaluate. $$Q=It$$ $$15=I \times 0.52$$ 2. Substitute the numbers and evaluate. $$Q=It$$ $$10=I \times 12 \times 10^{-3}$$ 3. Rearrange the equation and solve. $$I=\frac{15}{0.52}$$ $$I=28.846153A$$ $$I\approx29A$$ 3. Rearrange the equation and solve. $$I=\frac{10}{12 \times 10^{-3}}$$ $$I=833.3A$$ $$I\approx830A$$

#### Finding Charge from Current and Time

 A battery supplies 4.7Amps to a bulb over a period of 14 seconds. Calculate the charge leaving the battery in this time correct to two significant figures. A hairdryer uses a current of 7.2A for 5 minutes to dry a person’s hair. Calculate the charge flowing through the hairdryer in this time correct to two significant figures. 1. State the known quantities in correct units. I = 4.7A t = 14s 1. State the known quantities in correct units. I = 7.2A t = 5min = 300s 2. Substitute the numbers into the equation and solve. $$Q=It$$ $$Q=4.7 \times 14$$ $$Q = 65.8C$$ $$Q \approx 66C$$ 2. Substitute the numbers into the equation and solve. $$Q=It$$ $$Q=7.2 \times 300$$ $$Q = 2160C$$ $$Q \approx 2200C$$

#### Finding Time from Current and Charge

 A battery charger uses a current of 150mA to deliver a charge of 245 Coloumbs to a battery. Calculate the time taken to charge this battery correct to two significant figures. A cloud in a thunderstorm loses 15C in one lightening strike. At a current of 31,000kA. Calculate how long this lightning strike lasts correct to two significant figures. 1. State the known quantities in correct units. I = 150mA = 150x10-3A Q = 245C 1. State the known quantities in correct units. I = 31,000kA = 3.1x107A Q = 15C 2. Substitute the numbers and evaluate. $$Q=It$$ $$245 = 150 \times 10^{-3} \times t$$ 2. Substitute the numbers and evaluate. $$Q=It$$ $$15= 3.1 \times 10^7 \times t$$ 3. Rearrange the equation and solve. $$t=\frac{245}{150 \times 10^{-3}}$$ $$t=1633.3s$$ $$t\approx1633.3s$$ 3. Rearrange the equation and solve. $$t=\frac{15}{3.1 \times 10^7}$$ $$t = 4.8387 \times 10^{-7}s$$ $$t\approx4.8 \times 10^{-7}s$$

#### Finding Charge from Potential Difference and Energy Transferred

 The potential difference of 12V is placed across a resistor increasing its thermal energy store by 3.7J as a result. Calculate the charge that has flowed through the resistor in this time correct to two significant figures. A circuit transfers 2.8kJ of energy electrically to a motor. The potential difference across the motor is 1.5V. Calculate thecharge that has flowed through the motor in this time correct to two significant figures. 1. State the known quantities in correct units. V = 12V E = 3.7J 1. State the known quantities in correct units. V = 1.5V E = 2.8kJ = 2.8x103J 2. Substitute the numbers into the equation and solve. $$Q=\frac{E}{V}$$ $$Q=\frac{3.7}{12}$$ $$Q=0.3083C$$ $$Q\approx0.31C$$ 2. Substitute the numbers into the equation and solve. $$Q=\frac{E}{V}$$ $$Q=\frac{2.8 \times 10^3}{1.5}$$ $$Q=1866.7C$$ $$Q\approx1900C$$

#### Finding Potential Difference from Charge and Energy Transferred

 A charge of 84C transfers an energy of 20kJ. Calculate the potential difference correct to two significant figures. 170J of energy is transferred by a charge of 92mC. Calculate the potential difference correct to two significant figures. 1. State the known quantities in correct units. Q = 84C E = 20kJ = 20x103J 1. State the known quantities in correct units. Q = 92mC = 92x10-3C E = 170J 2. Substitute the numbers and evaluate. $$Q=\frac{E}{V}$$ $$84=\frac{20 \times 10^3}{V}$$ 2. Substitute the numbers and evaluate. $$Q=\frac{E}{V}$$ $$92 \times 10^{-3}=\frac{170}{V}$$ 3. Rearrange the equation and solve. $$V=\frac{20 \times 10^3}{84}$$ $$V=238.0952V$$ $$V\approx 240V$$ 3. Rearrange the equation and solve. $$V=\frac{170}{92 \times 10^{-3}}$$ $$V=1847.826V$$ $$V\approx 1800V$$

#### Finding Energy Transferred from Charge and Potential Difference

 A bolt of lightning with a potential difference 31,000kV transfers a charge of 15C. Calculate the energy transferred by this bolt of lightning correct to two significant figures. A 9V battery is able to mobilise a charge of 4.3kC during its operation. Calculate the total amount of energy stored in this battery correct to two significant figures. 1. State the known quantities in correct units. V = 31,000kV = 3.1x107V Q = 15C 1. State the known quantities in correct units. V = 9V Q = 4.3kC = 4.3x103 2. Substitute the numbers and evaluate. $$Q=\frac{E}{V}$$ $$15=\frac{E}{3.1 \times 10^7}$$ 2. Substitute the numbers and evaluate. $$Q=\frac{E}{V}$$ $$4.3 \times 10^3 =\frac{E}{9}$$ 3. Rearrange the equation and solve. $$E = 15 \times 3.1 \times 10^7$$ $$E = 4.65\times10^8 J$$ $$E\approx4.7\times10^8 J$$ 3. Rearrange the equation and solve. $$E = 4.3 \times 10^3 \times 9$$ $$E = 38700J$$ $$E \approx 39000 \times 10^4J$$