In electric circuits the potential energy supplied by the battery is converted
The energy transformation and its conservation inside a circuit can be understood by introducing another Physics quantity called power.
In general Power is defined as the energy developed per unit time. Using maths:
its unit of measurement is watt (W):
.
The power in the circuit can be found by recalling the definition of potential energy, the definition of the electric current, then by coupling them with the definition of Power we gave above.
by inserting the first relationship in the third we have
then by inserting the second the computation yields to
Hence, we can state that the power supplied by a battery with a potential
difference 
while connected to a
circuit, can be calculated by multiplying its voltage difference by the current 
flowing in the circuit.
If we couple the last relationship with Ohm’s law, we get other useful expressions for power:
this yields to
or yields to
.
Hence, in an Ohm circuit power can be written in three different ways
For instance, in order to compute the power dissipated by a resistor in a circuit we can use:
the expression (2) if we know the resistance of the component and the current flowing through it;
the expression (3) if we know the resistance and the loss in potential at the poles of the component.
Inside an electric circuit, the energy conservation principle can be easily stated by saying the power supplied by the battery equals the power dissipated by the components (appliances) connected to the circuit.
The power and current we use at home usually don’t come from a battery, they come from power lines delivering current from a distant power plant. The source of the energy depends on the plant producing it. For instance hydroelectric stations use the gravitational potential energy of water stored behind a dam; coal stations use the chemical potential energy stored in the fossil fuel; nuclear stations use the nuclear potential energy stored in Uranium; wind energy stations use the kinetic energy of the wind and so on.
In the case of chemical and nuclear fuels, the potential energy is converted to heat then used to run a heat engine like a steam turbine. In the case of hydroelectric stations, the water falling is used to run the turbine. In general all power plants use electric generators that convert the mechanical kinetic energy produced by the turbine to electric energy.
The transmission of electric energy to our homes involves the problem of transferring energy over a considerable distance. The problem is solved by changing the voltage of the current with transformers. As we will see, the transformation of voltage can easily be obtained only if the current is an alternate current. For this reason the current we draw from a wall outlet in our homes is alternate current (ac) rather than direct current (dc).
Alternate current continually reverses its direction. It flows first in one direction, than in the other then back again and so on. This behaviour can be described by using trigonometric function, like sine or cosine curve. (in general trigonometric functions are useful to describe all oscillating phenomena).
The frequency of oscillation of the current is measured in hertz.
.
The number of hertz means the number of oscillations the current makes back and forth per unit time (second). For instance in Europe the frequency of the current is
while in North America it is
.
The average value of an alternating current is zero because of the continuous and regular back and forth oscillations (see fig.13.17 on page 257 in the textbook). Anyway, because the power dissipated in a resistance has a square dependence on current and voltage (see the previous formula) it makes sense to use an average of the squared current to find the effective current of the circuit.
The effective alternate current is computed by:
Avoiding the (very complex) details, for a sinusoidal curve this process yields to the value
The same consideration can be applied to the voltage difference (see fig.13.18 on page 258 in the textbook)
We can use these values of the effective current and effective voltage to analyse alternating current circuits and to compute values of electric power as we did for direct current circuits.
Household circuits are always wired in parallel to assure that difference appliances can be added to (or removed from) the circuit without affecting the voltage available to each.
The total current drawn from the circuit increases as we add more appliances, (the total resistance decreases when resistances are added in parallel . Too large a current could cause the wires to overheat. To prevent this from happening a circuit breaker is in series with one leg of the circuit. If the current becomes too great the breaker disrupts the entire circuit and no current will flow to any of the attached appliances. (See fig.13.19 on page 260 of the textbook).
Looking at your electric bill, you have probably noted that the quantity of energy used for household applications is measured in kilowatt-hours.
The kilowatt-hour is a unit of measurement obtained by multiplying a unit of power (the kilowatt) by a unit of time (an hour). Since a kilowatt is 1000 watts and an hour is 3600 seconds, 1 kilowatt-hour equals 3.6 millions of joules.
The kilowatt-hour is a much larger unit of energy then the joule and it represents a convenient size for the amounts of electrical energy typically used in a home.
