The current of 10 amps approaching point B is divided into a 6-amp pathway through resistor 2 and a 4-amp pathway through resistor 3. Thus, it is seen that the current values in the three branches are 2 amps, 6 amps and 4 amps and that the sum of the current values in the individual branches is equal to the current outside the branches.
A flow analysis at points C and D can also be conducted and it is observed that the sum of the flow rates heading into these points is equal to the flow rate that is found immediately beyond these points. The actual amount of current always varies inversely with the amount of overall resistance. There is a clear relationship between the resistance of the individual resistors and the overall resistance of the collection of resistors. Since the circuit offers two equal pathways for charge flow, only one-half the charge will choose to pass through a given branch.
With three equal pathways for charge to flow through the external circuit, only one-third the charge will choose to pass through a given branch.
This is the concept of equivalent resistance. The equivalent resistance of a circuit is the amount of resistance that a single resistor would need in order to equal the overall effect of the collection of resistors that are present in the circuit.
For parallel circuits, the mathematical formula for computing the equivalent resistance R eq is. The examples above could be considered simple cases in which all the pathways offer the same amount of resistance to an individual charge that passes through it. The simple cases above were done without the use of the equation. Yet the equation fits both the simple cases where branch resistors have the same resistance values and the more difficult cases where branch resistors have different resistance values.
For instance, consider the application of the equation to the one simple and one difficult case below. It has been emphasized throughout the Circuits unit of The Physics Classroom tutorial that whatever voltage boost is acquired by a charge in the battery is lost by the charge as it passes through the resistors of the external circuit. The total voltage drop in the external circuit is equal to the gain in voltage as a charge passes through the internal circuit. In a parallel circuit, a charge does not pass through every resistor; rather, it passes through a single resistor.
Thus, the entire voltage drop across that resistor must match the battery voltage. It matters not whether the charge passes through resistor 1, resistor 2, or resistor 3, the voltage drop across the resistor that it chooses to pass through must equal the voltage of the battery. Put in equation form, this principle would be expressed as. If three resistors are placed in parallel branches and powered by a volt battery, then the voltage drop across each one of the three resistors is 12 volts.
A charge flowing through the circuit would only encounter one of these three resistors and thus encounter a single voltage drop of 12 volts. Electric potential diagrams were introduced in Lesson 1 of this unit and subsequently used to illustrate the consecutive voltage drops occurring in series circuits. An electric potential diagram is a conceptual tool for representing the electric potential difference between several points on an electric circuit.
Consider the circuit diagram below and its corresponding electric potential diagram. As shown in the electric potential diagram, positions A, B, C, E and G are all at a high electric potential. A single charge chooses only one of the three possible pathways; thus at position B, a single charge will move towards point C, E or G and then passes through the resistor that is in that branch.
The charge does not lose its high potential until it passes through the resistor, either from C to D, E to F, or G to H. Once it passes through a resistor, the charge has returned to nearly 0 Volts and returns to the negative terminal of the battery to obtain its voltage boost.
Unlike in series circuits, a charge in a parallel circuit encounters a single voltage drop during its path through the external circuit. The current through a given branch can be predicted using the Ohm's law equation and the voltage drop across the resistor and the resistance of the resistor.
Since the voltage drop is the same across each resistor, the factor that determines that resistor has the greatest current is the resistance. The resistor with the greatest resistance experiences the lowest current and the resistor with the least resistance experiences the greatest current.
In this sense, it could be said that charge like people chooses the path of least resistance. In equation form, this could be stated as. This principle is illustrated by the circuit shown below. Yet the current is different in each resistor. The current is greatest where the resistance is least and the current is least where the resistance is greatest. The above principles and formulae can be used to analyze a parallel circuit and determine the values of the current at and electric potential difference across each of the resistors in a parallel circuit.
Their use will be demonstrated by the mathematical analysis of the circuit shown below. The goal is to use the formulae to determine the equivalent resistance of the circuit R eq , the current through the battery I tot , and the voltage drops and current for each of the three resistors.
The analysis begins by using the resistance values for the individual resistors in order to determine the equivalent resistance of the circuit. Now that the equivalent resistance is known, the current in the battery can be determined using the Ohm's law equation. The calculation is shown here:. The 60 V battery voltage represents the gain in electric potential by a charge as it passes through the battery.
The charge loses this same amount of electric potential for any given pass through the external circuit. That is, the voltage drop across each one of the three resistors is the same as the voltage gained in the battery:.
There are three values left to be determined - the current in each of the individual resistors. Ohm's law is used once more to determine the current values for each resistor - it is simply the voltage drop across each resistor 60 Volts divided by the resistance of each resistor given in the problem statement. The calculations are shown below. As a check of the accuracy of the mathematics performed, it is wise to see if the calculated values satisfy the principle that the sum of the current values for each individual resistor is equal to the total current in the circuit or in the battery.
The 0. The mathematical analysis of this parallel circuit involved a blend of concepts and equations. As is often the case in physics, the divorcing of concepts from equations when embarking on the solution to a physics problem is a dangerous act. Here, one must consider the concepts that the voltage drops across each one of the three resistors is equal to the battery voltage and that the sum of the current in each resistor is equal to the total current.
These understandings are essential in order to complete the mathematical analysis. In the next part of Lesson 4 , combination or compound circuits in which some devices are in parallel and others are in series will be investigated.
Adding more resistors in parallel is equivalent to providing more branches through which charge can flow. Even though the added branches offer resistance to the flow of charge, the overall resistance decreases due to the fact that there are additional pathways available for charge flow.
The fraction of the total charge which encounters a single resistor is now less. The additional branches mean that the circuit can sustain a greater current. Total voltage of a parallel circuit has the same value as the voltage across each branch. A parallel circuit has more than one path for current flow. The number of current paths is determined by the number of load resistors connected in parallel. Total current in a parallel circuit is the sum of the individual branch currents.
To solve for the total current, you must first determine individual branch currents using Ohms law:. Electrical Circuits. Electrical Circuit Closed path through which charge can flow A Circuit needs: 1. Source of energy voltage 2. Conductive path for. Unit 8 - Circuits.
When diagramming circuits,. OBJ: Given images, video, activity sheet SWBAT describe the basic features of an electric circuit and explain how a series circuit differs from a parallel. Similar presentations. Upload Log in. My presentations Profile Feedback Log out. Log in. Auth with social network: Registration Forgot your password? Download presentation. Cancel Download. Presentation is loading. Please wait. Copy to clipboard.
Presentation on theme: "What kind of circuit do you see and how many paths so you see? Download ppt "What kind of circuit do you see and how many paths so you see? Cells in Series and Parallel Dry cells can be connected together into two basic types of circuits: series.
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