**Examples and exercises using V=R I and P=V I **

(V -voltage, I - current, R - resistance)

An electric current consists of electric charges in movement, which are usually (but not always) electrons inside a wire .

Electric charges move because of a **electric potential (or voltage)**. It is similar to objects moving down because of the gravitational potential.

A collection of electric charges moving is an **electric current**.

The higher the voltage, the larger the current. The intensity of the current also depends on the amount of charges available and on the **resistance** to movement . The higher the resistance, the more difficult for the electrons to move, the lower the current.

Although a metal wire is a medium where the electrons can move, it exerts some resistance against this movement. The resistance will depend on the temperature and also on the material out of which the wire is made. Copper, for instance, offers lower resistance than most metals. Aluminium is also a good conductor (although not as good as copper) and because it is cheaper than copper and light weight it is used in transmission lines (where we get very long and thick wires). If the temperature goe down, the resistance also goes down, and vice-versa.

Also, the more electrons in the wire, the higher the current.

The relationship between voltage (V), resistance(R) and current (I) is easily determined using Ohm's law: **V=RI** .

It can be rearranged, so that it becomes: I = V / R

Voltage is measured in volts (V), current is measured in amperes (A) and resistance is measured in ohms (Ω).

Some typical values of electric currents:

Human nervous system | 20 µA |

Train motor | 600 A |

Lightning | 10 to 100 kA |

One ampere (A) equals one coulomb per second (C/s).

**-Calculate the voltage needed to create an electric current of 10A in a circuit where the resistance is 10 Ω**

V=RI --> V=10*10 = 100 V

**-Calculate the current in a toaster that has a heating
element of 10 Ω when connected to a 220 V mains supply.**

I = V / R --> I= 220/10= 22 A

**- A light bulb in a car works with a voltage of 12V. If the current on it is 1 A, what is its resistance? **

V=RI --> R= V / I --> R = 12/1 = 12 Ω

An electric current can transport **energy**, and as a result, **power**.

Electrical power is the amount of electrical energy transferred per second.

The power of an electric system depends on the voltage and also on the current. If a system has high voltage and high current (example:lightning), the power developed will be high.

The relationship between electric power (measured in watts), voltage and current is very simple:

**P=V I **

Some common rearrangementes of this formulas are often useful to solve problems:

Substituting V=RI in the formula above we get

P = RI^{2}

Or substituting I = U/R:

P = U^{2}/R

**-What is the power developed by a car light bulb that works with 12 V and a current of 1.2 A ?**

P = UI = 12*1.2 = 14.4 W

**-Calculate the power of a hair dryer that operates on
220 volts and draws a current of 5 amperes.**

P = UI = 220*5 = 1100 W

**-If an electric shower has a power of 2000 W, and it is plugged in a 220 V mains. Calculate the current in its wires.**

P = UI --> I = P/V --> I = 2000/220 = 9.1 A

**-An electric shower has two settings: winter and summer, so that if winter is chosen the water comes out hotter than in the summer setting. What happens to the shower circuit when you switch from summer to winter?**

**a) the voltage increases**

**b)the voltage decreases**

**c)the resistance increases**

**d) the resistance decreases**

For this exercise is conveniente to use the rearranged power formula:

P = U^{2}/R

It shows clearly that if resistance is reduced, power increases.

so, the correct answer is d)