Why resistors in parallel

Why study Chemical Engineering at Cambridge? Resistors In Parallel. Introduction In the previous part we identified how the resistance of a circuit can be calculated when one or more resistors are combined in series. Identifying and Analysing Parallel Circuits When two or more resistors are connected between identical points in a circuit the resistors are said to be in parallel.

Each parallel current path is called a branch and if additional branches are added then more possible current paths are created eg In this circuit all the connecting points along the bottom rail are equivalent to B and all the connecting points along the top rail equivalent to point A. This states that the sum of the currents into a junction is equal to the sum of the currents out of the junction.

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When resistors are connected in parallel, the supply current is equal to the sum of the currents through each resistor. The currents in the branches of a parallel circuit add up to the supply current. When resistors are connected in parallel, they have the same potential difference across them. Any components in parallel have the same potential difference across them. In order to calculate the total resistance of two resistors connected in parallel, this equation is used.

The voltage across is. The voltage applied to and is less than the voltage supplied by the battery by an amount.

When wire resistance is large, it can significantly affect the operation of the devices represented by and. To find the current through , we must first find the voltage applied to it. The voltage across the two resistors in parallel is the same:. The current is less than the that flowed through when it was connected in parallel to the battery in the previous parallel circuit example. The power dissipated by is given by.

The analysis of complex circuits can often be simplified by reducing the circuit to a voltage source and an equivalent resistance. Even if the entire circuit cannot be reduced to a single voltage source and a single equivalent resistance, portions of the circuit may be reduced, greatly simplifying the analysis. Consider the electrical circuits in your home. Give at least two examples of circuits that must use a combination of series and parallel circuits to operate efficiently.

One implication of this last example is that resistance in wires reduces the current and power delivered to a resistor. If wire resistance is relatively large, as in a worn or a very long extension cord, then this loss can be significant. If a large current is drawn, the drop in the wires can also be significant and may become apparent from the heat generated in the cord. For example, when you are rummaging in the refrigerator and the motor comes on, the refrigerator light dims momentarily.

Similarly, you can see the passenger compartment light dim when you start the engine of your car although this may be due to resistance inside the battery itself. What is happening in these high-current situations is illustrated in Figure 6. The device represented by has a very low resistance, so when it is switched on, a large current flows.

This increased current causes a larger drop in the wires represented by , reducing the voltage across the light bulb which is , which then dims noticeably. Two resistors connected in series are connected to two resistors that are connected in parallel. The series-parallel combination is connected to a battery. Each resistor has a resistance of. The wires connecting the resistors and battery have negligible resistance.

A current of runs through resistor. What is the voltage supplied by the voltage source? Since they are in series, the current through equals the current through. Since , the current through each will be. The power dissipated by the resistors is equal to the sum of the power dissipated by each resistor:. Since the power dissipated by the resistors equals the power supplied by the battery, our solution seems consistent.

Significance If a problem has a combination of series and parallel, as in this example, it can be reduced in steps by using the preceding problem-solving strategy and by considering individual groups of series or parallel connections.

When finding for a parallel connection, the reciprocal must be taken with care. In addition, units and numerical results must be reasonable. Equivalent series resistance should be greater, whereas equivalent parallel resistance should be smaller, for example.

Power should be greater for the same devices in parallel compared with series, and so on. Skip to content By the end of the section, you will be able to: Define the term equivalent resistance Calculate the equivalent resistance of resistors connected in series Calculate the equivalent resistance of resistors connected in parallel.

Equivalent Resistance, Current, and Power in a Series Circuit A battery with a terminal voltage of is connected to a circuit consisting of four and one resistors all in series Figure 6. Analysis of a Parallel Circuit Three resistors , , and are connected in parallel. Strategy a The total resistance for a parallel combination of resistors is found using. Solution a. Entering known values gives The total resistance with the correct number of significant digits is. This gives Current for each device is much larger than for the same devices connected in series see the previous example.

Thus, Similarly, and The total current is the sum of the individual currents: d. Thus, Similarly, and e. Choosing and entering the total current yields Significance Total power dissipated by the resistors is also :.

Series combination Parallel combination Equivalent capacitance Equivalent resistance Table This results in a current of from the voltage source. Combining Series and Parallel Circuits Figure 6. The answer is that the large current the appliance motor draws causes a significant drop in the wires and reduces the voltage across the light.

Problem-Solving Strategy: Series and Parallel Resistors Draw a clear circuit diagram, labeling all resistors and voltage sources. This step includes a list of the known values for the problem, since they are labeled in your circuit diagram. Identify exactly what needs to be determined in the problem identify the unknowns. A written list is useful.

Determine whether resistors are in series, parallel, or a combination of both series and parallel. Examine the circuit diagram to make this assessment. Resistors are in series if the same current must pass sequentially through them. Use the appropriate list of major features for series or parallel connections to solve for the unknowns.

There is one list for series and another for parallel. Check to see whether the answers are reasonable and consistent. Combining Series and Parallel Circuits Two resistors connected in series are connected to two resistors that are connected in parallel.

Strategy Use the steps in the preceding problem-solving strategy to find the solution for this example.