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Series and Parallel Resistors

# Series and Parallel Resistors

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Simple circuits such as resistive elements connected in series or parallel are key components of complex electrical circuits.

Connecting resistors in series results in a division of voltage, while sharing the same current.

Conversely, when resistors are connected in parallel, it results in a division of current and the voltage across the resistors is the same. To understand the functioning of any electrical circuit, simple or complex, Ohm's law is used.

This video will cover the basics of connecting electrical resistive components in series and parallel, and explain the principles of calculating voltage and current for these circuits based on Ohm's law.

As per Ohm's Law, the current 'I' through a resistor of resistance 'R', is directly proportional to the voltage drop 'V' across the resistor or the voltage drop is the product of the resistance 'R' and the current 'I'.

If two resistors, R1 and R2, are connected in series, that is one after the other, then the same current flows through both resistors.

In this case, the total voltage drop 'V' is equal to the sum of the voltage drop across each resistor. On applying the Ohm's law for voltages V1 and V2, and since the currents are equal, we derive the total voltage drop as equal to the sum of resistances R1 and R2 times the current 'I'.

Moving I to the other side of the equation gives V/I, which, as per Ohm's law, is the total effective resistance of the circuit 'R'. Thus, 'R' is simply the sum of the individual resistances.

This rule is applicable for any number of resistors connected in series.

Conversely, if the two resistors, are connected in parallel, which means they are both wired between two shared terminals, then both resistors share the same voltage drop.

However, the total current 'I', is split between the resistors and is thus equal to the sum of individual currents of the circuit. Now, if we take this current equation, apply Ohm's law, cancel out the voltages on either side as they are equal for parallel resistors, and rearrange the equation for effective resistance 'R', we observe that R equals to the 'product-over-sum' of the two individual resistances

Let's go back to the equation before rearrangement. The inverse of resistance is conductance, 'G'. Therefore, for two parallel resistors, the effective conductance is equal to the sum of the two conductance values.

This rule can also be extended to multiple resistors connected in parallel.

The following experiment demonstrates the step-wise method of connecting resistors in either configuration and analyzing the circuits using the Ohm's Law.

To begin, gather the necessary materials and instruments, namely a current source, a voltage source, two multimeters, two 100-ohm resistors, two 10-ohm resistors, and a breadboard.

Using the breadboard, connect one end of a 100-ohm resistor to the output terminal of the current source. Then connect the other end of the 100-ohm resistor to the opposite terminal of the source.

Next, generate a 10-milli ampere current through the resistor and set the multimeter in voltage measurement mode. Now connect the two terminals of the multimeter to the two terminals of the resistor and measure the voltage drop across the resistor.

A positive reading means that the potential at the positive terminal of the multimeter is higher than that at the negative terminal. Using this voltage readout Ohm's law can be verified.

Next, apply a 1-volt voltage across the 100-ohm resistor. Now set the multimeter in current measurement mode. Connect the terminals of the multimeter in series with the resistor and measure the current through it.

A positive current reading means that the current is flowing from the positive terminal to the negative terminal of the multimeter. Using the measured current, Ohm's law can be verified.

Next, disconnect the voltage source from the resistor. Set the multimeter to resistance measurement mode. Connect the two terminals of the multimeter to the two terminals of the resistor and directly measure the resistance.

The measured resistance should re-verify Ohm's law and previously measured current and voltage measurements.

First, connect two 100-ohm resistors in series on the breadboard. Then connect them to the current source as described in the previous section and apply a 10-milli ampere current through both resistors.

Using the multimeter in voltmeter mode, measure the voltage drop across each resistor and across the entire series combination.

Next, apply a 10-volt voltage across both resistors. Then set the multimeter in the ammeter mode and measure the current through each resistor.

Connect two 100-ohm resistors in parallel. Then, connect them to a voltage source as described previously. Apply a 10-volt voltage across the resistors.

Using the multimeter in ammeter mode, measure the current through each resistor and through the entire parallel combination of resistors.

The brightness of lightbulbs depends not only on the voltage applied, but also on whether they are connected in series and/or with other components

Obtain two light emitting diodes or lightbulbs, each with resistance of few ohms, which can be used in place of the resistors. Connect one lightbulb to the voltage source as described previously. Apply a one-volt voltage across the lightbulb and observe its brightness.

Now, turn off the voltage source and connect the second lightbulb in parallel with the first. Apply a one-volt voltage across the parallel combination and observe the brightness of both lightbulbs.

Finally, turn off the voltage source and re-connect the lightbulbs in series. Apply a one-volt voltage across the series combination and observe the brightness of both lightbulbs.

Now that we have reviewed the protocols, let us look at the results of connecting resistors in series and parallel

The results from the series experiment show that, as per Ohm's law, the voltage across each resistor is directly proportional to the respective resistance. In addition, the voltage across both resistors is the sum of voltages across each resistor; whereas the current flowing through each resistor and through the combination is the same. Furthermore, the total resistance of the circuit is equal to the sum of the two individual resistances.

This proves the predicted voltage, current, and resistance relationships for a series combination.

On the other hand, when the resistors are connected in parallel, the current across each resistor is inversely proportional to the resistance, in accordance with the Ohm's law. Additionally, the total current flowing through the parallel combination is the sum of the individual currents, but the voltage across each resistor and across the combination is the same.

Lastly, if we convert the resistance values to conductance values, the results show that the total conductance of the circuit is equal to the sum of the two individual conductance values. This validates the theoretical voltage, current, and conductance relationships for a parallel combination.

When the lightbulbs are connected in series or parallel different levels of lightbulb brightness are observed. When lightbulbs are connected in parallel, both lightbulbs have similar brightness to the single lightbulb connected to the same voltage source.

This is because the lightbulbs are powered by voltage, and the ones connected in parallel each have the same voltage of 1 volt across them, as in the case of a single lightbulb.

On the other hand, the two lightbulbs connected in series are dimmer than the single lightbulb. This is because the two lightbulbs in series each receive only 0.5 V, as the voltage is split between them.

Series and parallel resistor connections are common in circuit applications. Let us now look at some examples where these are used.

A common application of series connection is a voltage divider circuit that converts a larger voltage into a smaller one. The input voltage is applied across two series resistors and the output voltage is obtained from the connection between them. Voltage division is the result of distributing the input voltage among the resistors of the divider circuit.

Commercial wiring in our homes, offices, labs and classrooms are setup so that multiple electrical appliances can be plugged in and used. This is possible because any electrical instrument, when plugged into the 110-volt outlet in the wall, is connected in parallel to all the other instruments that are already in use.

Thus, they all share the 110-volt common voltage and under normal operating conditions are able to operate without affecting other instruments.

You've just watched JoVE's introduction to Series and Parallel Resistors. You should now understand how to connect current and voltage sources, and measure various electrical circuit parameters using the multimeter. Additionally you should now also know how to connect resistances in series and parallel and analyze them using Ohm's Law. Thanks for watching! X 