1. Circuit Components

An electric circuit is formed when a conductive path is created allowing the free electrons of a source to constantly move around the conductor and elements related to him.

The serial and parallel arrangements of circuits are common for the study of electricity and electronics.

The element is a chemical source of electricity.

By adding multiple elements a battery is constructed.

Depending on the chemical reaction a battery can have different voltage values. The most common batteries have a voltage value of  about 1,5 V per chemical element. Also, according to their size they are categorized as ΑΑ, ΑΑΑ, C, D etc.

If you have an element of 3 Ah, providing 0.1 A current in a circuit, then this element will have a lifetime 30 hours.

1.1. Serial Arrangement

In serial circuits the current passing through all the elements has the same intensity. The elements are positioned adjacent to one another in series.

If four elements with 1,5V EMF each are connected in series then a battery of 6V EMF is created (4*1.5V).

This arrangement has the sum of the EMFs of all elements but provides the same power as a single element.

The schematic of this arrangement is represented as follows:

1.2. Parallel Arrangement

If four elements of 1.5 V are arranged in parallel, a 1.5 V battery is created, but it can provide up to four times of each element’s current intensity.

If the power provided by each element is 0,5 Amps (500 mA), then this arrangement can create a battery of 1.5 V and 2 Amps (4 x 0.5 = 2).

So, now a battery cell with these characteristics is created. If you use it as an element you can have a battery that can supply current of 6 Volts and 2 amps. How? By adding this element of high amperage and low voltage element in series with 3 similar elements.

2. Circuit Resistors

2.1. Resistors in Series

Let now examine the parallel and series arrangement  of resistors.

If two resistors of 2 kΩ are connected in series with an elements of 3 V, what can you calculate according to the schematic?

You know that the current passing through the circuit has the same amperage in all points of the circuit.

The voltage across each resistor should be the same, since each resistor has the same resistance and the same current flows through it.

The EMF source is the battery element of 3V. Therefore, each resistor will have a potential difference of 1.5 V across its length.

Provided that:

2.2. Resistors in Parallel

Now, let’s connect two resistors of 2 ΚΩ  in parallel with an element, according to the schematic:

Each resistor will have voltage value of 3V across its length. But which will the current intensity of each resistor be?

The total current of each element will be 2 × I_R, which is 3 mA.

2.3. Resistance of Resistors in Series or Parallel

You saw that that the intensity of the current is different in serial and parallel circuits, even when the same elements are used.

If there is only one resistor of 1 kΩ that is connected with a battery 1.5 V, then the current is of 1,5 mA.

If the resistors are connected in series, the current is reduced by half, 0.75 mA. This implies that the total resistance of the circuit should be doubled.

If the resistors are connected parallel the current doubles to 3 mA. This implies that the total resistance should be reduced by half.

In the following example the circuit is simplified since there are only two resistors with the same resistance value, so it is easy to calculate the current passing through the resistors.

When the circuits are more complex, the resistors are not of the same value, more general equations are needed that will allow to find the total resistance of the circuit, regardless of the resistor values.

3. Kirchhoff’s Laws

Kirchhoff’s circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits.

In an electric circuit Node is called the point of the circuit, where at least three conductors are met .

Loop is called the part of the circuit between two nodes.

Each closed circuit is called loop.

3.1. Kirchhoff’s first law, Kirchhoff’s point rule, or Kirchhoff’s junction rule (or nodal rule).

At any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node.

If you consider the I_i is positive and I_o is negative then the first rule of Kirchhoff can be expressed as:

The algebraic sum of currents in a network of conductors meeting at a point is zero.

3.2. Kirchhoff’s voltage law

The directed sum of the electrical potential differences (voltage) around any closed network is zero.

3.3. Resistors in Series

Three resistors of R₁, R₂ and R₃,are connected in series with a battery EMF V.

The R₁ voltage is V₁, the R₂ voltage is V₂ and the R₃ voltage is V₃.

According to Kirchhoff’s voltage law:

The same current, Ι, passes through all resistors. By replacing V with IR:

Simplifying gives:

Therefore:

V/Ι can be replaced by the R_T,  where R_T is the equivalent total resistance of the three resistors:

So the resistors in series can be replaced by a resistor with a resistance which is equal to the sum of their individual values.

3.4. Resistors in Parallel

Three resistors of R₁, R₂ and R₃,are connected in parallel with a battery EMF V.

The voltage across each resistor is V.

The R₁ current intensity is Ι₁, the R₂ current intensity is Ι₂, and the R₃ current intensity is Ι₃.

According to Kirchhoff’s junction rule (or nodal rule):

By replacing Ι with V/R then:

3.4.1. Resistors in Parallel – Equivalence

Simplifying gives:

Therefore:

Ι/V can be replaced by 1/R_T,  where R_T is the equivalent total resistance of the three resistors:

3.5. Resistors in Series And In Parallel

If the circuits containing resistors in series and parallel can be simplified by:

• By replacing the parallel resistors with their equivalent resistor.

• By replacing  any of the resistors in series with the equivalent resistor.

When the resistors are in series, the equivalent resistance is always higher than the largest resistor.

When the resistors are in parallel, the equivalent resistance is always lower than the smallest resistor.

Electrical Circuit: is an interconnection

(α) sources
(b) Consumer (ohmic resistors)
(c) Switches and capacitors that are connected by conductive wires of negligible resistance

Direct current (DC) is the unidirectional flow of electric charge. The electric current flows in a constant direction, particular circuit voltage or current does not depend on the past value of any circuit voltage or current.

There are two types of circuits:
In series, Components connected in series are connected along a single path, so the same current flows through all of the components

In parallel, Components are connected so the same voltage is applied to each component

Each integrated circuit requires a power source. For our experiments we will use either the power supply of the mobile laboratory or batteries.

Action: With the cables of the batteries or of the power supply connect the positive pole (red) to the port 1 of the electric board 1 and the negative pole (black) to the port 2 of the electric board.

Action: Close the circuit by using 2 banana clip cables. Connect one from port 3 to 7 and the other from port 4 to 8. See the picture.

Action: Turn on the switch.

Effect: If the lamp turns on, then your circuit is successfully connected.

Create a circuit of two lamps in series.

In the same way create a circuit of 3 lamps in series.

Action: Remove a lamp and check if the current flows through the circuit.

Effect: By disconnecting a lamp the circuit is not closed so the current does not flow through it.

Create a circuit of two lamps in parallel.

In the same way create a circuit of three lamps in parallel.

Action: Remove a lamp and check if the current flows through the circuit.

Effect: This time the disconnection of a lamp does not affects the other lamps. The circuit remains closed and the rest lamps are on.

In this experiment we are going to measure the potential difference across circuits both serial and parallel. In order to do that we will use a digital multimeter. Make sure that is set for direct current of up to 20 V.

In a circuit a voltmeter is always positioned in parallel to take measurements, and it’s resistance is very high in order to leave unaffected the electric current.

To make measurements we can use alligator clips as in images where they are connected with the multimeter probes or we can put the probes directly inside the jacks if we don’t mind using both hands.

Let’s make a simple circuit with one lamp.

Action: Turn on the switch and place the probes of the multimeter at 7 and 8 positions of the board as explained earlier.

Effect: We should see our measurement at the display.

Create a circuit with two lamps and measure the potential difference in each lamp and record your results.

Repeat your measurements with 3 lamps in serial too. Notice also how the glowing has been reduced with every lamp addition.

The sum of voltages of each lamp should be equal to the voltage our batteries give to the circuit V = V₁ + V₂ + V₃.

We know that the electric current is constant for all the circuit, so how we determine the voltage of each lamp (or resistor) using Ohm’s law?

Let V₁ and R₁ be the voltage and the resistance for the first lamp, and V₂, V₃,  R₂, R₃ for the second and third. Then it is:

V₁  = I * R₁

V₂ = I * R₂

V₃ = I * R₃

If we put V₁, V₂, V₃ and R₁, R₂, R₃ in a graph we will see they have a linear relationship.

Action: Try to disconnect the third lamp removing a clip lead, measure again the potential difference in every lamp and record your results.

Effect: This break simulated a lamp in the circuit being blown, as a result all the lamps stopped glowing.

Now on to the parallel circuits.

Create a circuit with two lamps as in image. Use the multimeter as usual to measure the potential difference of each lamp and record your results.

If we compare our results with those from the serial circuits we can see that the parallel setup is better as the voltages in each lamp are as high as the batteries provide, this is also apparent in the illumination of the lamps.

Action: Try to disconnect the third lamp removing a clip lead, measure again the potential difference in every lamp and record your results.

Effect: As we can see lamp 1 and 3 are working just fine, by disconnecting the 2^nd lamp in the circuit only that particular lamp stopped illuminating. This is a clear advantage over circuits in series.

1. Create the circuit in the picture below which contains the resistor (R1) of the electric board 2, a current sensor connected in series and a voltage sensor connected in parallel with the source.

2. Connect the data logger DL120RS to the PC via USB port and the voltage and current sensors to the Data logger via a UTP cable into the ports #1 and #2.

3. Run the i lab software and select “Setup“ at the main menu.

Make sure that the “DL120RS” interface is selected.

4.a. Download and open the i lab Experiment Setup file found here:

4.a.1. Jump to step 14

OR

4.b. Select “Start” at the i lab main menu. It will open the experiment screen.

5. At the experiment screen you can see the following areas:

7. Then from the window “Select display mode” select Custom template (bottom right).

8. On the left of the screen appears an options bar. Select “View diagram” and twice consecutively “Show meter”. Each selection populates a new form window on the Experiment area.

9. Reorder and rename (by right-clicking the title) the windows properly, as shown in the image below.

11. At the new window that appears (Curve editor) we can edit the curves that will be displayed in the Diagram form.

Fill in the fields as in the picture below so that voltage is displayed at the x axis and current at the y axis.

Finally, click on the “Add” button.

12. Right-click inside the Voltage Meter Display window and select the voltage variable in V.

13. Repeat the same for the second measurement window and select current. The final forms will be as follows:

The curve is expressed by a straight line type y = ax + b where a = -r b = E. The inclination of the curve depends on the constant a that is the internal resistance of the source.

When the source has no current, the electromotive force E is equal to the voltage V_p at the poles of the source.

The physical significance of the point of curve intersection with the current axis is the maximum current that can flow through the source which is called short circuit current.

If you connect the poles of the source with a conductor of negligible resistance, ie R=0, then we say that the source is short circuited. Using Ohm’s Law:

16. Create the circuit in the following picture which contains a battery, the resistor (R1) of the electric board 2, a current sensor connected in series and a voltage sensor connected in parallel with the resistor.

The curve is expressed by a straight line type y = ax. So, it obeys Ohm’s law where:

The slope of the line expresses the value

If the graph was I = f(V) then the physical meaning of the curve inclination would be