 # Power Formula

## What is Power?

The capacity to do work is termed Energy. The Energy expended to do work in unit time is termed as Power. It is represented as P.

Power Formula is articulated as,

$$\begin{array}{l}P = \frac{E}{t}\end{array}$$
$$\begin{array}{l}P = \frac{W}{t}\end{array}$$

or,

Where,
The Energy Consumed to do work = E
Work done =
Time taken=

In any electrical circuit, the power is computed making use of these three formulas

In regard to Voltage and current, it is articulated as

P = V×I

In regard to current and resistance, it is articulated as

P = I2R

In regard to voltage and resistance, it is articulated as

$$\begin{array}{l}P = \frac{V^{2}}{R}\end{array}$$

Where,
A voltage applied across the two ends =V,

Current flowing in the circuit = I and
Resistance = R.

The Power Formula is used to compute the Power, Resistance, Voltage or current in an electrical circuit. The standard metric unit of power is the Watt.

### Solved Examples

Problem 1: An electric machine makes use of 300 J of energy to do work in 10s. How much power does it use?

Known: Work done = W = 300 J,
Time taken t = 10 s.

Power used by it is given by

$$\begin{array}{l}P=\frac{W}{t}=\frac{300J}{10s}=30Watts\end{array}$$

Problem 2: John is who has a mass of 60 kg runs up to 12m high in 40 seconds. Compute his power.

Known: m (mass) = 60 kg,
h (Height) = 12 m,
t (time taken) = 40 seconds.

Power is given by:

$$\begin{array}{l}P=\frac{work\;done}{time\;taken}\end{array}$$

P=mgh/t

$$\begin{array}{l}=\frac{60 \times 9.8 \times 12}{40} = 588 Watts\end{array}$$

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