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Law of total probability provides a formula for the probability of any event in terms of conditional probabilities in a partitioned sample space.Suppose A is any event defined in the sample space S. Since there are multiple paths for the supply current to flow through, the current may not be the same through all the branches in the parallel network.
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. 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.
In the previous series resistor network we saw that the total resistance, RT of the circuit was equal to the sum of all the individual resistors added together.
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. If the two resistances or impedances in parallel are equal and of the same value, then the total or equivalent resistance, RT is equal to half the value of one resistor. Note that the equivalent resistance is always less than the smallest resistor in the parallel network so the total resistance, RT 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.
We now know that resistors that are connected between the same two points are said to be in parallel. The five resistive networks above may look different to each other, but they are all arranged as Resistors in Parallel and as such the same conditions and equations apply. This method of reciprocal calculation can be used for calculating any number of individual resistances connected together within a single parallel network.
If however, there are only two individual resistors in parallel then we can use a much simpler and quicker formula to find the total or equivalent resistance value, RT and help reduce the reciprocal maths a little. The total current, IT entering a parallel resistive circuit is the sum of all the individual currents flowing in all the parallel branches. For example, although the parallel combination has the same voltage across it, the resistances could be different therefore the current flowing through each resistor would definitely be different as determined by Ohms Law.
Calculate the individual branch currents and total current drawn from the power supply for the following set of resistors connected together in a parallel combination.
As the supply voltage is common to all the resistors in a parallel circuit, we can use Ohms Law to calculate the individual branch current as follows. This total circuit current value of 5 amperes can also be found and verified by finding the equivalent circuit resistance, RT of the parallel branch and dividing it into the supply voltage, VS as follows.



The equivalent or total resistance, RT of a parallel combination is found through reciprocal addition and the total resistance value will always be less than the smallest individual resistor in the combination. Thus far we have seen resistor networks connected in either a series or a parallel combination. If you’ve ever taken an Economics class you may recognize the meaning behind the blue curve above. So, here’s to staying on the left hand side of the curve and continuing to learn as much as we can. What is TEC?The True Entrepreneur Corps is a fellowship program developed by True Ventures to pair undergraduate students with portfolio companies for a summer of learning and innovation.
Resources, Tools and Basic Information for Engineering and Design of Technical Applications! When the angle of incidence in water reaches a certain critical value, the refracted ray lies along the boundary, having an angle of refraction of 90-degrees. Unlike the previous series resistor circuit, in a parallel resistor network the circuit current can take more than one path as there are multiple paths for the current. However, the voltage drop across all of the resistors in a parallel resistive network IS the same. Then in our parallel resistor example below the voltage across resistor R1 equals the voltage across resistor R2 which equals the voltage across R3 and which equals the supply voltage.
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. In other words, the equivalent resistance of a parallel network will always be less than the smallest individual resistor in the combination.
But the amount of current flowing through each parallel branch may not necessarily be the same, as the resistive value of each branch determines the amount of current flowing within that branch. So a parallel resistor circuit having N resistive networks will have N-different current paths while maintaining a common voltage across itself. When two or more resistors are connected so that both of their terminals are respectively connected to each terminal of the other resistor or resistors, they are said to be connected together in parallel. Parallel resistor networks can be interchanged within the same combination without changing the total resistance or total circuit current.
In the next tutorial about Resistors, we will look at connecting resistors together in both a series and parallel combination at the same time producing a mixed or combinational resistor circuit.
The curve represents the Law of Diminishing Returns and it suggests there is a point (the middle phase in the graph above) when adding one more employee to a company will result in a smaller increase in productivity than the previous employee (marginal return of labor).


This angle of incidence is known as the critical angle; it is the largest angle of incidence for which refraction can still occur. Then, Resistors in Parallel have a Common Voltage across them and this is true for all parallel connected elements.
To convert conductance back into a resistance value we need to take the reciprocal of the conductance giving us then the total resistance, RT of the resistors in parallel. However, we do know that the current that enters the circuit at point A must also exit the circuit at point B. Parallel resistors can also be interchanged with each other without changing the total resistance or the total circuit current. The voltage across each resistor within a parallel combination is exactly the same but the currents flowing through them are not the same as this is determined by their resistance value and Ohms Law. Resistors connected together in a parallel circuit will continue to operate even though one resistor may be open-circuited. It even suggests that there is a point further down the line where adding another employee will actually result in lower total productivity (think of the phrase too many chefs in the kitchen).
Rather than going to that event on building a lean startup that you’ve learned about already, consider going to a design talk that teaches you the impact of color on customer behavior. For any angle of incidence greater than the critical angle, light will undergo total internal reflection.
If you still don’t fully understand the concept, then check out a more in-depth explanation here. By building your portfolio of skills, you’ll be able to learn more and make the most of your time. This is great for you because you can mold these questions around concepts that you are still eager to learn about and that the speaker may be in an expert in.
The next time you feel that way, take a minute, think about what the event really has to offer, and then, if you really believe you’ll learn, make a decision to go or not to go. The process of finding the probability of an event using partition and conditional probability is also called the method of conditioning. That being said, I do think there are ways to make sure that you stay on the left hand side of the curve.



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