Electric Energy Formula

The amount of electrical energy consumed by an appliance can be easily calculated, and so can the cost of this energy consumption. Electrical energy is transferred to an appliance based on its power rating and the duration it is operated. This energy transfer is typically measured in kilowatt-hours (kWh), which is a standard unit of electrical energy.

Electrical Energy Calculations

The electrical energy transferred to an appliance depends on two main factors: the power of the appliance and the time it is used. The relationship between these factors is given by the following formula:

$$E = P \times t$$

Where:

• ( E ) is the energy transferred in kilowatt-hours (kWh),
• ( P ) is the power in kilowatts (kW),
• ( t ) is the time in hours (h).

Note that power is measured in kilowatts here instead of the more usual watts. To convert from watts (W) to kilowatts (kW), you must divide by 1,000:

$$1,000\, \text{W} = \frac{1,000}{1,000} = 1\, \text{kW}$$

Time is usually measured in hours, but if it is provided in seconds, you can convert it by dividing by 3,600:

$$7,200\, \text{s} = \frac{7,200}{3,600} = 2\, \text{h}$$

Ohm’s Law

One of the most important principles in electric energy is Ohm’s Law. It states that:

“At a constant temperature, the current through a conductor is directly proportional to the potential difference across the points.”

This can be mathematically expressed as:

$$V = I \times R$$

Where:

• ( V ) is the voltage in volts (V),
• ( I ) is the current in amperes (A),
• ( R ) is the resistance in ohms (Ω).

Formula for Calculating Power from Electrical Energy

The formula that links energy and power is:

$$\text{Energy} = \text{Power} \times \text{Time}$$

The unit of energy is the joule (J), the unit of power is the watt (W), and the unit of time is the second (s). For example, if a 40-watt lamp is turned on for one hour, the energy consumption is calculated as follows:

$$\text{Energy} = 40\, \text{W} \times 3,600\, \text{s} = 144,000\, \text{Joules}$$

Formula for Calculating Current

Current can be calculated using the formula:

$$I = \frac{Q}{t}$$

Where:

• ( I ) is the current in amperes (A),
• ( Q ) is the charge in coulombs (C),
• ( t ) is the time in seconds (s).

Example: If 15 C of charge passes through the circuit in 3 seconds, the current is:

$$I = \frac{15\, \text{C}}{3\, \text{s}} = 5\, \text{C/s}$$

Voltage

Voltage, often described as the ‘force’ that pushes current through a circuit, is measured by the following formula:

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

Where:

• ( V ) is the voltage in volts (V),
• ( W ) is the work done in joules (J),
• ( Q ) is the charge in coulombs (C).

Example: If the energy transferred is 35 J, and the charge is 15 C, the voltage is:

$$V = \frac{35\, \text{J}}{15\, \text{C}} = 2.33\, \text{V}$$

Examples of Electric Energy

Example: Heat Produced by an Electric Iron

Calculate the heat produced by an electric iron, which has a resistance of 30 ohms and takes a current of 3 amperes when it is switched on for 15 seconds.

Step 1: Calculate Power

$$\text{Power} = I^2 \times R = 3^2 \times 30 = 270\, \text{W}$$

Step 2: Calculate Energy

$$\text{Energy} = \text{Power} \times \text{Time} = 270\, \text{W} \times 15\, \text{s} = 4,050\, \text{Joules}$$

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