Calculating voltage and current in series and parallel circuits pdf

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Published: 05.05.2021  Series And Parallel Circuits Worksheet Answer Key Pdf

Most circuits have more than one resistor. If several resistors are connected together and connected to a battery, the current supplied by the battery depends on the equivalent resistance of the circuit. The equivalent resistance of a combination of resistors depends on both their individual values and how they are connected.

In a series circuit , the output current of the first resistor flows into the input of the second resistor; therefore, the current is the same in each resistor.

In a parallel circuit , all of the resistor leads on one side of the resistors are connected together and all the leads on the other side are connected together. In the case of a parallel configuration, each resistor has the same potential drop across it, and the currents through each resistor may be different, depending on the resistor.

The sum of the individual currents equals the current that flows into the parallel connections. Resistors are said to be in series whenever the current flows through the resistors sequentially. Since there is only one path for the charges to flow through, the current is the same through each resistor.

The equivalent resistance of a set of resistors in a series connection is equal to the algebraic sum of the individual resistances. The current through the circuit depends on the voltage supplied by the voltage source and the resistance of the resistors. For each resistor, a potential drop occurs that is equal to the loss of electric potential energy as a current travels through each resistor. Since energy is conserved, and the voltage is equal to the potential energy per charge, the sum of the voltage applied to the circuit by the source and the potential drops across the individual resistors around a loop should be equal to zero:.

Any number of resistors can be connected in series. One result of components connected in a series circuit is that if something happens to one component, it affects all the other components.

For example, if several lamps are connected in series and one bulb burns out, all the other lamps go dark. Assume the battery has negligible internal resistance. In a series circuit, the equivalent resistance is the algebraic sum of the resistances.

There are several reasons why we would use multiple resistors instead of just one resistor with a resistance equal to the equivalent resistance of the circuit. Perhaps a resistor of the required size is not available, or we need to dissipate the heat generated, or we want to minimize the cost of resistors. Each resistor may cost a few cents to a few dollars, but when multiplied by thousands of units, the cost saving may be appreciable.

Some strings of miniature holiday lights are made to short out when a bulb burns out. The device that causes the short is called a shunt, which allows current to flow around the open circuit.

The bulbs are usually grouped in series of nine bulbs. If too many bulbs burn out, the shunts eventually open. What causes this? The equivalent resistance of nine bulbs connected in series is 9 R.

As more bulbs burn out, the current becomes even higher. Eventually, the current becomes too high, burning out the shunt. Resistors are in parallel when one end of all the resistors are connected by a continuous wire of negligible resistance and the other end of all the resistors are also connected to one another through a continuous wire of negligible resistance.

The potential drop across each resistor is the same. The same is true of the wiring in your house or any building.

The sum of the currents flowing into a junction must be equal to the sum of the currents flowing out of the junction:. When resistors are connected in parallel, more current flows from the source than would flow for any of them individually, so the total resistance is lower.

Note that in these calculations, each intermediate answer is shown with an extra digit. Notice that the total power dissipated by the resistors equals the power supplied by the source. Would the equivalent resistance of the series circuit be higher, lower, or equal to the three resistor in parallel? Would the current through the series circuit be higher, lower, or equal to the current provided by the same voltage applied to the parallel circuit?

How would the power dissipated by the resistor in series compare to the power dissipated by the resistors in parallel? The equivalent resistor of any number of resistors is always higher than the equivalent resistance of the same resistors connected in parallel. This is not surprising since the equivalent resistance of the series circuit is higher. The current through a series connection of any number of resistors will always be lower than the current into a parallel connection of the same resistors, since the equivalent resistance of the series circuit will be higher than the parallel circuit.

How would you use a river and two waterfalls to model a parallel configuration of two resistors? How does this analogy break down? A river, flowing horizontally at a constant rate, splits in two and flows over two waterfalls.

The water molecules are analogous to the electrons in the parallel circuits. The number of water molecules that flow in the river and falls must be equal to the number of molecules that flow over each waterfall, just like sum of the current through each resistor must be equal to the current flowing into the parallel circuit. The water molecules in the river have energy due to their motion and height. The potential energy of the water molecules in the river is constant due to their equal heights.

This is analogous to the constant change in voltage across a parallel circuit. Voltage is the potential energy across each resistor. The analogy quickly breaks down when considering the energy. In the waterfall, the potential energy is converted into kinetic energy of the water molecules. In the case of electrons flowing through a resistor, the potential drop is converted into heat and light, not into the kinetic energy of the electrons.

In this chapter, we introduced the equivalent resistance of resistors connect in series and resistors connected in parallel. Circuits often contain both capacitors and resistors.

More complex connections of resistors are often just combinations of series and parallel connections. Such combinations are common, especially when wire resistance is considered. In that case, wire resistance is in series with other resistances that are in parallel. Various parts can be identified as either series or parallel connections, reduced to their equivalent resistances, and then further reduced until a single equivalent resistance is left.

The process is more time consuming than difficult. They can be combined into a single equivalent resistance. One method of keeping track of the process is to include the resistors as subscripts. Those two resistors can be reduced to an equivalent resistance:. Here, the circuit reduces to two resistors, which in this case are in series.

These two resistors can be reduced to an equivalent resistance, which is the equivalent resistance of the circuit:. The main goal of this circuit analysis is reached, and the circuit is now reduced to a single resistor and single voltage source. Now we can analyze the circuit. The final analysis is to look at the power supplied by the voltage source and the power dissipated by the resistors. The power dissipated by the resistors is.

The total energy is constant in any process. Therefore, the power supplied by the voltage source is. Analyzing the power supplied to the circuit and the power dissipated by the resistors is a good check for the validity of the analysis; they should be equal. 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. All the overhead lighting circuits are in parallel and connected to the main supply line, so when one bulb burns out, all the overhead lighting does not go dark. Each overhead light will have at least one switch in series with the light, so you can turn it on and off.

A refrigerator has a compressor and a light that goes on when the door opens. There is usually only one cord for the refrigerator to plug into the wall.

The circuit containing the compressor and the circuit containing the lighting circuit are in parallel, but there is a switch in series with the light. A thermostat controls a switch that is in series with the compressor to control the temperature of the refrigerator.

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 IR 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.

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 2. What is the voltage supplied by the voltage source? Use the steps in the preceding problem-solving strategy to find the solution for this example. 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. 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. In addition, units and numerical results must be reasonable. Equivalent series resistance should be greater, whereas equivalent parallel resistance should be smaller, for example. Simple Series Circuits

There are two types of circuits: a series and a parallel circuit. Explain your observations. Create your own tracing worksheets with our interactive worksheet maker. However, to add more than one bit of data in length, a parallel adder is used. Free kindergarten to grade 6 math worksheets, organized by grade and topic. Such a device is shown schematically in Fig. What is the capacitance of the capacitors when combined in parallel? Series And Parallel Circuits Worksheet Answer Key Pdf

The first principle to understand about parallel circuits is that the voltage is equal across all components in the circuit. This is because there are only two sets of electrically common points in a parallel circuit, and the voltage measured between sets of common points must always be the same at any given time. Therefore, in the above circuit, the voltage across R 1 is equal to the voltage across R 2 which is equal to the voltage across R 3 which is equal to the voltage across the battery.

Parallel circuilts have constant Voltage. The following three appliances are connected in series to a V house circuit: a toaster, Two resistors in parallel and the resulting total resistance: Two of the same value, also show the equation that the results are always half. A series circuit comprises a path along which the whole current flows through each component.

Skip to main content. Search form Search. Series and parallel circuits gcse worksheet. Series and parallel circuits gcse worksheet series and parallel circuits gcse worksheet 5V Parallel circuits The potential difference voltage across each component connected in parallel is the same. The amount of current in a series circuit is the same through any component in the circuit. This is because there is only one path for current flow in a series circuit. Because electric charge flows through conductors like marbles in a tube, the rate of flow marble speed at any point in the circuit tube at any specific point in time must be equal.

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The amount of current in a series circuit is the same through any component in the circuit. This is because there is only one path for current flow in a series circuit. Because electric charge flows through conductors like marbles in a tube, the rate of flow marble speed at any point in the circuit tube at any specific point in time must be equal. From the way that the 9-volt battery is arranged, we can tell that the current in this circuit will flow in a clockwise direction, from point 1 to 2 to 3 to 4 and back to 1. However, we have one source of voltage and three resistances.

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