# Work and Power

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## Work and Power

As electricity is all about energy, there are a few energy and power equations that you need to be able to derive and use...

**So, W = VQ**

The definition of current tells us that, Q = It

**So, W = V I t (Learn this!)**

Of course, we already know that:

**So, Power = V I (Learn this!)**

From Ohm's law we know that V = IR. If this equation is substituted into the equation P = IV we can get two new equations:

**Power = I ^{2}R**

**Learn these!**

Electrical energy is measured in units of the kWhr so that people can be charged for the amount that they use. At the moment, 1 kWhr of energy costs about 7p.

**energy = power x time**

**kWhr = kW x hr**

When supplying electricity to people's home it is important that as little energy as possible is wasted as the electricity travels through the power lines and cables on the National Grid.

**So what is the best way to raise efficiency and reduce the amount of energy lost in the cables?**

You know that the greater the resistance of the cables the greater the power loss, so cables need to be made from good conductors and have as large a cross-sectional area as possible.

From P = V^{2}/R = I^{2}R we can see that the efficiency will be greatest when the voltages are high and the currents are low.

**Example:****If a power of 20 MW is to be delivered down a cable with resistance 100Ω, is it better to use:**

- a current of 20 A and a voltage of 1MV or
- a current of 2 A and a voltage of 10 MV

**Answer:**- Power wasted in the cable = I
^{2}R = 20 x 20 x 100 = 40 000 W - Power wasted in the cable = I
^{2}R = 2 x 2 x 100 = 400 W

It's clear that, for the same power to be delivered, reducing the current and increasing the voltage gives less wasted energy as the current flows through the cable. **Transformers** are used to step-up the voltage from the power station to the power lines and to step-down the voltage from the power lines to people's homes.

The problem of energy wastage has to be taken into consideration when looking at the applications of electricity. For instance, when transmitting electrical signals for communication, the signal loses strength as energy is lost in the cables.