What is the difference between equivalent resistance and total resistance

The circuit now reduces to three resistors, shown in Figure 6. Redrawing, we now see that resistors and constitute a parallel circuit. Those two resistors can be reduced to an equivalent resistance:. This step of the process reduces the circuit to two resistors, shown in in Figure 6. 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 current provided by the voltage source is. This current runs through resistor and is designated as. Looking at Figure 6. The resistors and are in series so the currents and are equal to. The potential drops are and. 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.

We can consider to be the resistance of wires leading to and a Find the equivalent resistance of the circuit. Then use this result to find the equivalent resistance of the series connection with. The current through is equal to the current from the battery. The voltage across can be found using. To find the equivalent resistance of the circuit, notice that the parallel connection of R 2 R2 and R 3 R3 is in series with R 1 R1 , so the equivalent resistance is.

The total resistance of this combination is intermediate between the pure series and pure parallel values and , respectively. The current through is equal to the current supplied by the battery:.

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. 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.

The 1. There are an infinite possibilities of I 2 and I 3 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. In this example, the unequal current in the two resistors complicates the analysis.

The branch with the least resistance will have the greatest current. Determining the amount of current will demand that we use the Ohm's law equation. But to use it, the voltage drop across the branches must first be known. So the direction that the solution takes in this example will be slightly different than that of the simpler case illustrated in the previous example.

To determine the voltage drop across the parallel branches, the voltage drop across the two series-connected resistors R 1 and R 4 must first be determined. This circuit is powered by a volt source. Thus, the cumulative voltage drop of a charge traversing a loop about the circuit is 24 volts. There will be a The voltage drop across the branches must be 4. The two examples above illustrate an effective concept-centered strategy for analyzing combination circuits. The approach demanded a firm grasp of the series and parallel concepts discussed earlier.

Such analyses are often conducted in order to solve a physics problem for a specified unknown. In such situations, the unknown typically varies from problem to problem. In one problem, the resistor values may be given and the current in all the branches are the unknown. In another problem, the current in the battery and a few resistor values may be stated and the unknown quantity becomes the resistance of one of the resistors. Different problem situations will obviously require slight alterations in the approaches.

Nonetheless, every problem-solving approach will utilize the same principles utilized in approaching the two example problems above. The following suggestions for approaching combination circuit problems are offered to the beginning student:. For further practice analyzing combination circuits, consider analyzing the problems in the Check Your Understanding section below. A combination circuit is shown in the diagram at the right. Use the diagram to answer the following questions. Equivalent Resistance vs Effective Resistance.

Resistance is a very important property of electrical and electronic circuits. The concept of resistance plays a vital role in fields such as electrical engineering, electronic engineering and physics.

It is vital to have a clear understanding of resistance and related subjects in order to be successful in such fields. In this article, we are going to discuss what equivalent resistance and effective resistance are, their definitions, the applications of equivalent resistance and effective resistance, the similarities between these two, and finally the difference between equivalent resistance and effective resistance. In order to understand the concept of equivalent resistance, one must first understand the concept of resistance.

The resistance, in a qualitative definition, tells us how hard it is for an electrical current to flow. Parallel combinations are often used to deliver more current. The output, or terminal voltage of a voltage source such as a battery, depends on its electromotive force and its internal resistance. Express the relationship between the electromotive force and terminal voltage in a form of equation. When you forget to turn off your car lights, they slowly dim as the battery runs down.

Their gradual dimming implies that battery output voltage decreases as the battery is depleted. The reason for the decrease in output voltage for depleted or overloaded batteries is that all voltage sources have two fundamental parts—a source of electrical energy and an internal resistance.

All voltage sources create a potential difference and can supply current if connected to a resistance. On a small scale, the potential difference creates an electric field that exerts force on charges, causing current. We call this potential difference the electromotive force abbreviated emf.

Emf is not a force at all; it is a special type of potential difference of a source when no current is flowing. Units of emf are volts. Electromotive force is directly related to the source of potential difference, such as the particular combination of chemicals in a battery.

However, emf differs from the voltage output of the device when current flows. The voltage across the terminals of a battery, for example, is less than the emf when the battery supplies current, and it declines further as the battery is depleted or loaded down. The voltage output of a device is measured across its terminals and is called its terminal voltage V. Terminal voltage is given by the equation:. Schematic Representation of a Voltage Source : Any voltage source in this case, a carbon-zinc dry cell has an emf related to its source of potential difference, and an internal resistance r related to its construction.

Note that the script E stands for emf. Also shown are the output terminals across which the terminal voltage V is measured. I is positive if current flows away from the positive terminal. The larger the current, the smaller the terminal voltage.

Likewise, it is true that the larger the internal resistance, the smaller the terminal voltage. Privacy Policy. Skip to main content. Circuits and Direct Currents. Search for:. Resistors in Series and Parallel. Resisitors in Series The total resistance in the circuit with resistors connected in series is equal to the sum of the individual resistances. Learning Objectives Calculate the total resistance in the circuit with resistors connected in series.

Key Takeaways Key Points The same current flows through each resistor in series. Individual resistors in series do not get the total source voltage, but divide it. Key Terms series : A number of things that follow on one after the other or are connected one after the other.

Resistors in Parallel The total resistance in a parallel circuit is equal to the sum of the inverse of each individual resistances. Learning Objectives Calculate the total resistance in the circuit with resistors connected in parallel. Key Takeaways Key Points The total resistance in a parallel circuit is less than the smallest of the individual resistances.

Each resistor in parallel has the same voltage of the source applied to it voltage is constant in a parallel circuit.