## Rl series to parallel conversion

Take this series-parallel circuit for example:. The first order of business, as usual, is to determine values of impedance Z for all components based on the frequency of the AC power source. To do this, we need to first determine values of reactance X for all inductors and capacitorsthen convert reactance X and resistance R figures into proper impedance Z form:. Being a series-parallel combination circuit, we must reduce it to a total impedance in more than one step.

The first step is to combine L and C 2 as a series combination of impedances, by adding their impedances together.

Then, that impedance will be combined in parallel with the impedance of the resistorto arrive at another combination of impedances. Finally, that quantity will be added to the impedance of C 1 to arrive at the total impedance. In order that our table may follow all these steps, it will be necessary to add additional columns to it so that each step may be represented.

Adding more columns horizontally to the table shown above would be impractical for formatting reasons, so I will place a new row of columns underneath, each column designated by its respective component combination:.

This time, there is no avoidance of the reciprocal formula: the required figures can arrive at no other way! This gives us one table with four columns and another table with three columns. Now that we know the total impedance At this point we ask ourselves the question: are there any components or component combinations which share either the total voltage or the total current?

That last step was merely a precaution. In a problem with as many steps, as this one has, there is much opportunity for error. Occasional cross-checks like that one can save a person a lot of work and unnecessary frustration by identifying problems prior to the final step of the problem. In this case, the resistor R and the combination of the inductor and the second capacitor L—C 2 share the same voltage, because those sets of impedances are in parallel with each other.

Therefore, we can transfer the voltage figure just solved into the columns for R and L—C 2 :. Another quick double-check of our work at this point would be to see if the current figures for L—C 2 and R add up to the total current. Since the L and C 2 are connected in series, and since we know the current through their series combination impedance, we can distribute that current figure to the L and C 2 columns following the rule of series circuits whereby series components share the same current:.

With one last step actually, two calculationswe can complete our analysis table for this circuit. As you can see, these figures do concur with our hand-calculated figures in the circuit analysis table. As daunting a task as series-parallel AC circuit analysis may appear, it must be emphasized that there is nothing really new going on here besides the use of complex numbers.

While there is more potential for human error in carrying out the necessary complex number calculations, the basic principles and techniques of series-parallel circuit reduction are exactly the same. In Partnership with Newark. Don't have an AAC account? Create one now. Forgot your password? Click here. Latest Projects Education. Textbook Series-parallel R, L, and C. Home Textbook Vol. The only substantive difference is that all figures and calculations are in complex not scalar form.By Patrick Hoppe.

Students view the formulas to be used to convert a series impedance to a parallel impedance. Click here to login. Sensor Hysteresis. By Terry Bartelt. Students read about the concepts of saturation and cutoff. They view diagrams that illustrate the interaction of the load line and the family of curves.

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In this animated object, learners examine the operation of a demultiplexer along with the data output and select lines.

A brief quiz completes the activity. Inductive Proximity Sensor Target Considerations. Learners consider the factors that determine how well an inductive proximity sensor can detect an object. Those factors are size, position, and the material from which the target is made. Inductive Reactance Practice Problems.

Students solve problems on the determination of total inductive reactance of series-parallel inductors. Capacitive Reactance Practice Problems. Students solve problems on the determination of total capacitive reactance of series-parallel capacitors.

AC Voltage Conversion Problems. By John Rosz, Terry Bartelt. AC Voltage Conversions. In this animated object, learners examine the formulas used to convert peak, RMS, average, and peak-to-peak AC voltages. By playing a game of tic-tac-toe, a student can review what happens to currents and voltages throughout a series RLC circuit when the applied frequency is increased from 0 Hz towards resonance. Cylinders: Basic Terminology. Creative Commons Attribution-NonCommercial 4.

Lecture 34: Non-ideal inductor, Inductor Q and series RL to parallel RL conversion

Sensor Hysteresis By Terry Bartelt. In this animated object, learners examine the hysteresis function of a sensor. Watch Now. More Less. Demultiplexers By Terry Bartelt.Random converter. This series RL circuit impedance calculator determines the impedance and the phase difference angle of an inductor and a resistor connected in series for a given frequency of a sinusoidal signal. The angular frequency is also determined. Example: Calculate the impedance of a mH inductor and a 0.

Enter the resistance, inductance and frequency values, select the units and click or tap the Calculate button. Try to enter zero or infinitely large values to see how this circuit behaves. Infinite frequency is not supported.

To enter the Infinity value, just type inf in the input box. To calculate, enter the inductance, the resistance and the frequency, select the units of measurements and the result for RL impedance will be shown in ohms and for the phase difference in degrees.

The inductive reactance in ohms will also be calculated. A simple series RL or resistor-inductor circuit is composed of a resistor and an inductor connected in series and driven by a voltage source. The current in both inductor and resistor is the same because they are connected in series. The voltages across the resistor V R and the inductor V L are shown in the diagram at the right angle to each other.

Their sum is always greater than the total voltage V T. If you look at the equation for calculating the impedance aboveyou will notice that it looks like the equation for calculating the hypotenuse of a right triangle.

This is because the impedance of an RL circuit in graphical form looks like in this picture where the resistance R is on the horizontal axes and the reactance X L is on the vertical axis. The hypotenuse is the impedance of the circuit and the phase angle is the angle between the horizontal axis and the impedance vector. From the reactance triangle. In a series RL circuit, the same current I flows through both the inductor and the resistor. From Kirchhoff's voltage law, the sum of the voltage drops must equal the total voltage V T.

Note that the total voltage is always less than the sum of the voltages across the resistor and the inductor — exactly like in any right-angle triangle where the length of the hypotenuse is shorter than the sum of the two legs of the triangle. Note also that it is impossible to measure impedance directly using an ordinary multimeter — you have to use an impedance meter for this purpose. An example of use is measurement of the impedance of several speakers with transformers, voice coils and crossovers.

Unlike a multimeter, which applies direct voltage to the circuit being measured, the impedance meter applies the AC test signal to the circuit being tested. What if something goes wrong in this circuit?

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Click or tap a corresponding link to view the calculator in various failure modes:. Various direct current modes. Short circuit.We recommend downloading the newest version of Flash here, but we support all versions 10 and above. If that doesn't help, please let us know.

### Series/Parallel RL Network Conversion Calculator

Unable to load video. Please check your Internet connection and reload this page. If the problem continues, please let us know and we'll try to help. An unexpected error occurred. Source: Yong P. Capacitors Cinductors Land resistors R are each an important circuit element with distinct behaviors.

A resistor dissipates energy and obeys Ohm's law, with its voltage proportional to its current. A capacitor stores electrical energy, with its current proportional to the rate of change of its voltage, while an inductor stores magnetic energy, with its voltage proportional to the rate of change of its current. When these circuit elements are combined, they can cause the current or voltage to vary with time in various, interesting ways. Such combinations are commonly used to process time- or frequency-dependent electrical signals, such as in alternating current AC circuits, radios, and electrical filters.

This experiment will demonstrate the time-dependent behaviors of the resistor-capacitor RCresistor-inductor RLand inductor-capacitor LC circuits. The experiment will demonstrate the transient behaviors of RC and RL circuits using a light bulb resistor connected in series to a capacitor or inductor, upon connecting to and switching on a power supply.

The experiment will also demonstrate the oscillatory behavior of an LC circuit. Physics II. Consider a resistor with resistance R in series of a capacitor with capacitance Ctogether connected to a voltage source with voltage output Vas depicted in Figure 1.

This current is also known as the "charging current" for the capacitor, as it "flows into" the capacitor i.

## Series-to-parallel impedance transformation

Equation 1. As time proceeds, charges build up on the capacitor and V c will increase, and thus i t will decrease. Furthermore, these charges tend to repel additional charges arriving at the capacitor i. This means that the capacitor is now fully charged or has the full voltage V from the voltage source dropping across itno more current flows, and the capacitor behaves as an open switch in this fully charged, steady state.

In general, a capacitor conducts more for higher frequency or transient current, while it conducts less or not at all for lower frequency or steady state DC current.

The full, quantitative time-dependent current i t can be solved by:. Equation 2. Equation 3. Such a time dependent current as given by Equation 2 is depicted in Figure 1. In this case, the RC time also represents the characteristic time scale for charging the capacitor.

It is the time scale for discharging a capacitor, namely, if a fully charged capacitor with voltage V is directly connected to a resistor to form a closed circuit corresponding to replacing the voltage supply in Figure 1 by a short wirethen the current flowing through the resistor will again follow Equation 2. An analogous analysis can be made for a resistor in series of an inductor, or an "RL" circuit such as the one shown in Figure 2.

However, the behavior of an inductor is opposite to that of a capacitor, in the sense that the inductor conducts better at lower frequency for steady state current the inductor acts as a short wire with little resistancebut conducts much less at higher frequency or in a transient situation because an inductor always tries to oppose the change in its current.

Equation 4. Equation 5. The exponential time dependence in the RC or RL circuit is related to the dissipative nature of the resistor. In contrast, an "LC" circuit where a capacitor is directly connected to an inductor with negligible resistances, such as the one shown in Figure 3awould exhibit an oscillatory or "resonant" behavior.In the fourth part of our series on Tips For Practicing Technicians, we look at a simple technique that can be used to simplify circuit analysis when working with series and parallel RL circuits.

One of the issues encountered by technicians who are working with parallel RL circuits is the need to work with values that are the reciprocals of the more commonly used standard units. The use of conductance, susceptance, and admittance instead of resistance, reactance, and impedance, can often cause confusion or uncertainty when working with these lesser employed units. Reducing such a mixed topology network down to a few inductors and resistors in series greatly simplifies calculating overall resistance and inductance in a given circuit or network.

In the series format, it is simply a matter of addition when calculating total inductive reactance, total resistance to get to overall impedance. Below are the basic equations for creating a series representation of a given parallel RL circuit.

Step 3 : Calculate the required inductor value that will provide the appropriate series inductive reactance for a given frequency. Step 4 : Redraw the circuit in a series configuration using the arrived at component values for the inductor and resistor. Correctly employing the above steps will result in a series representation of a parallel RL circuit that behaves identically with respect to voltage, current, and the phase relationship between them. From the perspective of points A and B in the above, both circuits will result in identical behaviour.

Employing topology conversion techniques such as Parallel to Series RL circuit conversion, Delta-Wye conversions for resistor networks, or simple Source Transformations converting current sources with parallel resistances to voltage sources with series resistances is a common simplification tactic that can be extremely helpful in circuit reduction and analysis at a technician level.

As a technician, the more tools you have at your disposal, the easier it will be to simplify and reduce complex circuits down to simple representations. This in turn will serve to reduce the chance of errors when performing technician level circuit analysis. In the animation below, an example of performing the conversion from a parallel RL circuit to an equivalent series RL circuit is illustrated step by step when the resistance and inductive reactance is known for the given parallel RL circuit.

We hope this has been helpful to you as a practicing or student technician. We are looking for other ideas for this continuing Practicing Technician series. Search Search. Performing the conversion Step 1 : Calculate the equivalent resistance value Rs Step 2 : Calculate the equivalent inductive reactance Xs Step 3 : Calculate the required inductor value that will provide the appropriate series inductive reactance for a given frequency.

Your name. About text formats. Save Preview.Objectives: 1. To practice equivalent circuit reduction techniques. To verify equivalence by using voltage, current, and phase measurements. Equipment and Components: 1. Function Generator 2. Oscilloscope 3. Other Resistors and Capacitors as Required.

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Procedures: 1. Draw the impedance diagram. Calculate measured current and total impedance using measured voltage and resistance values. Construct the series equivalent circuit found for step 3. Use voltage and current measurements to demonstrate equivalence. Determine the simplest parallel equivalent circuit that could replace the series circuit of step 3.

Construct the parallel equivalent circuit found in step 5, then use voltage and current measurements to demonstrate equivalence. Construct the parallel equivalent circuit found for step 9. In section one hand calculations were performed to find all the circuits voltages and currents I Vr Vc Vi. Once all impedance's were known ohms law E.

Following the hand calculations the circuit see Figure 1 was constructed and data taken to compare with the mathematical predictions made in section 1. The input signal and peek to peek voltage was set using a function generator and confirmed by the use of an oscilloscope. Measured voltages were taken using an oscilloscope and by applying ohms law E. Section three involved determining the simplest series equivalent circuit that could replace the circuit in Figure 1.

First the total impedance, Zt was calculated see Table 2. Next Zt was broken down into two specific elements.

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A real element being that of a resistor equaling ohms and an imaginary element, in this case a capacitor with an impedance of By knowing the impedance of the capacitor and the given frequency of 2kHz the capacitors value was calculated using the following equation.

Figure 4: Series Equivalent Circuit Figure 5: 0. Even though the new circuit see Figure 4 appears different from the original circuit see Figure 1the total voltages and currents within the circuit must equal that of the original circuit to be a true equivalent replacement.

Again a 4. In construction of the series equivalent circuit a small problem arose in that a 0. The series equivalent circuit was then constructed, measurements taken and compared to the original circuit's outputs see Table 3. Next the simplest parallel equivalent circuit was determined to replace the circuit in Figure 1. Although this is the total impedance for a series equivalent circuit.By Patrick Hoppe.

Students view the formulas to be used to convert a parallel impedance to a series impedance. Click here to login. This unit covers transformers. Waveforms of an SCR Circuit. By Terry Bartelt. Learners view waveforms at various locations of an SCR circuit controlling the intensity a light bulb.

The waveforms are shown when the light is dim, at medium brightness, and at full brightness. A brief quiz completes the activity. Series-Parallel Practice Problems Circuit 4. Diode Approximations. Inductive Reactance Practice Problems.

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Students solve problems on the determination of total inductive reactance of series-parallel inductors. Capacitive Reactance Practice Problems. Students solve problems on the determination of total capacitive reactance of series-parallel capacitors.

AC Voltage Conversion Problems. By John Rosz, Terry Bartelt. AC Voltage Conversions. In this animated object, learners examine the formulas used to convert peak, RMS, average, and peak-to-peak AC voltages. By playing a game of tic-tac-toe, a student can review what happens to currents and voltages throughout a series RLC circuit when the applied frequency is increased from 0 Hz towards resonance.