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Parallel Circuits Combination Circuits Previously in Lesson 4it was mentioned that there are two different ways to connect two or more electrical devices together in a circuit.
They can be connected by means of series connections or by means of parallel connections. When all the devices in a circuit are connected by series connections, then the circuit is referred to as a series circuit.
When all the devices in a circuit are connected by parallel connections, then the circuit is referred to as a parallel circuit. A third type of circuit involves the dual use of series and parallel connections in a circuit; such circuits are referred to as compound circuits or combination circuits.
The circuit depicted at the right is an example of the use of both series and parallel connections within the same circuit. In this case, light bulbs A and B are connected by parallel connections and light bulbs C and D are connected by series connections.
This is an example of a combination circuit. When analyzing combination circuits, it is critically important to have a solid understanding of the concepts that pertain to both series circuits and parallel circuits.
Since both types of connections are used in combination circuits, the concepts associated with both types of circuits apply to the respective parts of the circuit. The main concepts associated with series and parallel circuits are organized in the table below. Series Circuits The current is the same in every resistor; this current is equal to that in the battery.
The sum of the voltage drops across the individual resistors is equal to the voltage rating of the battery. Parallel Circuits The voltage drop is the same across each parallel branch. The sum of the current in each individual branch is equal to the current outside the branches. Each of the above concepts has a mathematical expression.
Analysis of Combination Circuits The basic strategy for the analysis of combination circuits involves using the meaning of equivalent resistance for parallel branches to transform the combination circuit into a series circuit.
Once transformed into a series circuit, the analysis can be conducted in the usual manner. Previously in Lesson 4the method for determining the equivalent resistance of parallel are equal, then the total or equivalent resistance of those branches is equal to the resistance of one branch divided by the number of branches.
If the two or more resistors found in the parallel branches do not have equal resistance, then the above formula must be used. An example of this method was presented in a previous section of Lesson 4. By applying one's understanding of the equivalent resistance of parallel branches to a combination circuit, the combination circuit can be transformed into a series circuit.
Then an understanding of the equivalent resistance of a series circuit can be used to determine the total resistance of the circuit. Consider the following diagrams below. Diagram A represents a combination circuit with resistors R2 and R3 placed in parallel branches.
This is shown in Diagram B. Now that all resistors are in series, the formula for the total resistance of series resistors can be used to determine the total resistance of this circuit: Once the total resistance of the circuit is determined, the analysis continues using Ohm's law and voltage and resistance values to determine current values at various locations.
The entire method is illustrated below with two examples. The first example is the easiest case - the resistors placed in parallel have the same resistance. The goal of the analysis is to determine the current in and the voltage drop across each resistor.
As discussed above, the first step is to simplify the circuit by replacing the two parallel resistors with a single resistor that has an equivalent resistance.
In doing so, the total resistance and the total voltage or battery voltage will have to be used. Yet, resistors R1 and R4 are in series and the current in series-connected resistors is everywhere the same.
There are an infinite number of possible values of I2 and I3 that satisfy this equation.
Since the resistance values are equal, the current values in these two resistors are also equal. Therefore, the current in resistors 2 and 3 are both equal to 2 Amp. These calculations are shown below. The second example is the more difficult case - the resistors placed in parallel have a different resistance value.
The goal of the analysis is the same - to determine the current in and the voltage drop across each resistor.
As discussed above, the first step is to simplify the circuit by replacing the two parallel resistors with a single resistor with an equivalent resistance. There are an infinite possibilities of I2 and I3 values that satisfy this equation.
In the previous example, the two resistors in parallel had the identical resistance; thus the current was distributed equally among the two branches.Description— The mackerel is fusiform in outline, tapering rearward to a very slim caudal peduncle and forward to a pointed nose.
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Analysis of Combination Circuits. The basic strategy for the analysis of combination circuits involves using the meaning of equivalent resistance for parallel branches to transform the combination circuit into a .
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