Electric current and electric circuits

What is the electric current?

In Physics the word "current" means "the flow of particles through a certain surface over time".

For instance, standing on a bridge we can talk about the "current of the river", that means, we are referring to the particles of water that flow under the bridge as the time passes.

Therefore an Electric Current is simply the flow of charged particles over time. It is a flow of particles that have the peculiarity of being charged.

By calling "" the electric current we can write in a more compact way

     definition of the electric current.

the unit of measurement of the current is C/s: we call this unit Ampere A=C/s.

We can produce an electric current using a battery and placing a metal wire between its terminals (plus and minus) in order to get a closed loop (a circuit). This way the electrons (negatively charged particles) can flow from the negative pole through the wire and join the positive particles stored at the positive terminal. The process goes on until the depletion of the reactants into the battery.

With such a circuit we short-circuit the battery and we discharge it very quickly. The only result of such an action is that we heat the wire.

If, on the contrary, we place an element in the circuit, (for example a light bulb) the battery lasts longer, because an element in the circuit provides a greater resistance to the flow of the particles.

In particular a bulb lamp consists of a thin filament through which the current passes. This filament restricts the amount of charge that can flow in the circuit, it represents a "bottleneck" in the circuit.

Because of the current forced into it, it gets very hot and emits light.

The Ohm's law

In general we can say that the amount of current that can flow depends strictly on the size of the wire: the thicker the wire the easier the passage of the current, because there is little resistance; the narrower  the wire, the harder  the passage of the current, because in this situation the resistance is higher.

As expected, the size of the current depends on the potential difference of the battery too. In fact, It’s the battery that provides the energy to push the electrons in the circuit.

The higher the voltage of the battery, the higher the current in the circuit and vice versa.

The law connecting all these facts is a proportional law. In the 1800’s Georg Ohm, discovered and stated that:

The current produced in a portion of wire by a certain potential difference, is directly proportional to the potential difference applied and inversely proportional to the resistance of the wire (Ohm’s Law)

If we label the "resistance of the wire" with the letter,  Ohm’s statement can be resumed by writing:

From a different point view Ohm’s law, provides a quantitative definition of the resistance of the wire:

In fact if we reverse the equation we get

that means resistance is the ratio of potential difference to the current.

Its unit of measurement is the Ohm

See the example in the text under the fig.13.6 on page 248.

Schematic of an electric circuit

In order to represent a circuit like the one in the figure, we can sketch its main components using standardized symbols.

The battery is sketched by drawing its two terminals: the longer line is the plus while the shorter and thicker line is the minus.

The bulb lamp and in general the resistors (components that provides a resistance to the passage of the current) are represented by a zigzagged line.

Electric wires are just straight lines, and we make the assumption they don’t provide resistance to the passage of the current.

The switch is represented by a break in the circuit: "closing the circuit" is equal to pushing the switch on and the net result is a current flowing. On the contrary, if the loop remains open the current can’t flow, (this is what happens when we turn the switch off).

See example 13.8 page 250 in the text-book.

Series circuits

In a circuit, we can insert more than one element one behind the other (See figure 13.9 in the text-book). This kind of circuit is called a series circuit, because all the components are placed in a consequential chain along a single loop arrangement. The same current passes through each component. The higher the number of components in the series, the  smaller the current flowing through. This happens because the total resistance of the circuit increases. In a series circuit if we have, for instance, three resistors with resistance the total resistance of the circuit is simply the sum of the single resistances:

.

If we have more than one light bulb in the series, they glow less brightly than a single bulb, because the total series resistance is larger.

Another defect of such an arrangement occurs when a bulb burns out: when the filament of a bulb breaks, all the circuit breaks and also the other bulbs go out. This is undesirable, and it makes it very hard to find the burned-out bulb.

Parallel circuits

In order to avoid the previous problems we can connect the bulbs in parallel (see fig.13.10 pag.252 in the textbook). In a parallel circuit we have more than one loop, and the current splits up into different path.

The main features of a parallel circuit are:

1. The total resistance decreases because we provide more than one flowing path and the current can flow easier than in a series circuit. The effective parallel resistance can be calculated with the formula

As the textbook says is the reciprocal of the sum of the reciprocal of each resistance, this yields a value less than any of the individual resistance(see the example on page 253 in the text-book).

2. In a parallel arrangement the voltage difference across each resistor is the same: all the elements are connected to the same points A and B.
3. The current in every single branch of the circuit can be different. A larger current will flow in the branch with the smaller resistance and vice-versa.

The main advantages of such a circuits are:

• It doesn’t matter how many elements we insert in the circuit, They all work all the time in the best way, because they are all connected to the same potential difference supplied by the battery.
• If an element goes out of order the current continues to flow through the others and the circuit doesn’t stop working!

The multimeter

The multimeter (fig. 13.11 page 254) lets us to measure the quantities involved in the physics description of an electric circuit like resistance, potential difference, and electric current. In effect it contains different instruments at the same time. By setting its function selector it can work as:

• An Ohmmeter: If we place its leads to the terminals of a resistor we can measure the resistance (Ohm) of the resistor.
• A Voltmeter: By placing its leads in parallel with the resistor we can measure the potential difference (Volt) between the terminals of the component (fig.13.12 page 254 on the textbook). The Voltmeter has a large resistance so that it doesn’t divert much current from the component whose voltage is being measured.
• An Ammeter: By placing its lead in series with the circuit it’s possible to measure the current (Ampere). The Ammeter has a small resistance in order to limits its effect on the current we want to measure. (fig.13.13 page 254 in the textbook).

Exercise

For the circuit in the following figure,

Find:

1. The current through the 4 ohm resistance;
2. The voltage difference across the AB parallel;
3. The current through the 2 ohm resistance.

1. The current through the 4 ohm resistance is equal to the total current of the circuit and we can calculate it with the Ohm’s law:

can be computed using the rules for the parallel and series resistances: by looking at the circuit we have

where

hence

.

so we conclude that

2. the voltage difference across the AB parallel is computed with the Ohm’s law too:

3. the current through the 2 ohm resistance is equal to the current passing through the upper branch of the circuit. Ohm’s law leads us to write the relationship

.

Some other interactive exercises can also be found at

http://www.clarkson.edu/~svoboda/eta/DCTutor/tutor2.html