BLOG 4 - ELECTRICAL CIRCUIT 1

THIS BLOG CONTAIN ABOUT SERIES AND PARALLEL RESISTOR

Resistors in Series

   Resistors are said to be connected in Series, when they are daisy chained together in a single line. Since all the current flowing through the first resistor has no other way to go it must also pass through the second resistor and the third and so on. Then, resistors in series have a Common Current flowing through them as the current that flows through one resistor must also flow through the others as it can only take one path.

Then the amount of current that flows through a set of resistors in series will be the same at all points in a series resistor network. For example:

 

In the following example the resistors R₁, R₂ and R₃ are all connected together in series between points A and B with a common current, I flowing through them.

Series Resistor Circuit

 

As the resistors are connected together in series the same current passes through each resistor in the chain and the total resistance, R_T of the circuit must be equal to the sum of all the individual resistors added together. That is

and by taking the individual values of the resistors in our simple example above, the total equivalent resistance, R_EQ is therefore given as:

 R_EQ = R₁ + R₂ + R₃ = 1kΩ + 2kΩ + 6kΩ = 9kΩ

Equivalent resistance  

Equivalent resistance of any number of resistors connected in series is the sum of the individual resistance.

Resistors in Parallel

Resistors are said to be connected together in “Parallel” when both of their terminals are respectively connected to each terminal of the other resistor or resistors. Unlike the previous series resistor circuit, in a parallel resistor network the circuit current can take more than one path as their are multiple nodes. Then parallel circuits are current dividers.

Since there are multiple paths for the supply current to flow through, the current is not the same at all points in a parallel circuit. However, the voltage drop across all of the resistors in a parallel resistive network is the same. Then, Resistors in Parallel have a Common Voltage across them and this is true for all parallel connected elements.

So we can define a parallel resistive circuit as one where the Resistors are connected to the same two points (or nodes) and is identified by the fact that it has more than one current path connected to a common voltage source. Then in our parallel resistor example below the voltage across resistor R₁equals the voltage across resistor R₂ which equals the voltage across R₃ and which equals the supply voltage. Therefore, for a parallel resistor network this is given as:

 

In the following resistors in parallel circuit the resistors R₁, R₂ and R₃ are all connected together in parallel between the two points A and B as shown.

Parallel Resistor Circuit

 

In the previous series resistor network we saw that the total resistance, R_T of the circuit was equal to the sum of all the individual resistors added together. For resistors in parallel the equivalent circuit resistance R_T is calculated differently.

Here, the reciprocal ( 1/R ) value of the individual resistances are all added together instead of the resistances themselves with the inverse of the algebraic sum giving the equivalent resistance as shown.

Parallel Resistor Equation

 

Then the inverse of the equivalent resistance of two or more resistors connected in parallel is the algebraic sum of the inverses of the individual resistances. The equivalent resistance is always less than the smallest resistor in the parallel network so the total resistance, R_T will always decrease as additional parallel resistors are added.

Parallel resistance gives us a value known as Conductance, symbol G with the units of conductance being the Siemens, symbol S. Conductance is the reciprocal or the inverse of resistance, ( G = 1/R ). To convert conductance back into a resistance value we need to take the reciprocal of the conductance giving us then the total resistance, R_T of the resistors in parallel.

We now know that resistors that are connected between the same two points are said to be in parallel. But a parallel resistive circuit can take many forms other than the obvious one given above and here are a few examples of how resistors can be connected together in parallel.

Equivalent Conductance

Equivalent conductance of resistors connected in parallel is the sum of their individual conductance.

Equivalent Resistance

Equivalent resistance of two resistor is equal to the product of their resistance divided by their sum.

LABORATORY

Objective:

• To measure the voltage and current in a resistor.

Materials:

• DC Power Supply 

• Digital Multimeter

• Resistor

• Breadboard 

Overview and learning 

   Last Monday we had our quiz it was about ohms law, kirchhoff’s current law (KCL) and kirchhoff’s voltage law (KVL). On the next day we had our laboratory experiment and some of our classmates discussed about bread boarding on how to use. My group mates also discussed about we had our experiment and use material such dc power supply, digital multi meter, connection wires, resistor and bread boarding. We measure voltage and current in order to know if it flows to the bread board. I also learned how to put a resistor and connecting wire in the bread board correctly. Last Wednesday our professor discussed about the series and parallel resistor and last Friday we had our seatwork and it was about parallel and series resistor.