# 4.3.2 Electrical Energy

### Electrical Energy Transfer

• The electrical power is also defined as the rate of change of work done: • The work done is the energy transferred
• The power is, therefore, the energy transferred per second in an electrical component
• Rearranging the energy and power equation, the energy can be written as:

W = Pt = IVt

• Where:
• W = Work done / energy transferred (J)
• P = power (W)
• V = voltage (V)
• I = current (A)
• t = time (s)

### Calculating the Cost of Energy & The Kilowatt-hour (kWh)

• The power of an appliance is:

The amount of energy transferred (by electrical work) to the device every second The power consumption of an electrical appliance can be found on a label that looks like this. This kettle uses between 2500 and 3000 W of electrical energy

• This energy is commonly measured in kilowatt-hour (kW h), which is then used to calculate the cost of energy
• This is used to calculate electricity bills
• A kilowatt-hour is defined as:

A unit of energy equal to 1 kW of power sustained for 1 hour

• Or as an equation:

Energy (kW h) = Power (kW) × Time (h)

• Since the usual unit of energy is joules (J), this is the 1 W in 1 s
• Therefore:

1 kW h = 1000 W × 3600 s = 3.6 × 106 J

• Since 1 kW = 1000 W and 1 h = 3600 s
• To convert between Joules and kW h:

kW h  × (3.6 × 106) = J

J  ÷ (3.6 × 106) = kW h

• The kW h is a large unit of energy, and mostly used for energy in homes

#### Worked Example

A cooker transfers 1.2 × 109 J of electrical energy to heat. How much will this cost if 1 kW h costs 14.2p?

Step 1: Convert from J to kW h

(1.2 × 109) ÷ (3.6 × 106) = 333.333 kW h

Step 2: Calculate the price

1 kW h = 14.2 p

333.333 × 14.2 = 4733 p = £47.33

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