Figure 11 : Physical wiring to measure total resistance of RL circuit. Lab 7 - LR Circuits Introduction The English physicist Michael Faraday found in that when the current through a coil changes, the coil produces a changing magnetic field in addition to the field of the changing currentwhich induces an electromotive force "emf" in the coil itself.

Inthe German physicist Heinrich Lenz refined this further by showing that the induced current driven by this emf will be in the direction that opposes the change in the original current.

We call this phenomenon self-inductionand the coils are called inductors. At the time that Faraday announced his discovery, he was asked what possible use such knowledge could be? His reply was: "Of what use is a newborn baby?

Inductors, like capacitorsaffect the time characteristics of an AC alternating current circuit and are, therefore, used to tune radio circuits, filter out unwanted noise, etc.

The telephone receiver makes use of a type of inductor, as do stereo speaker systems and microphones. In this lab you will examine the effect of an inductor on the current and voltage in a simple circuit. Discussion of Principles The inductance of a circuit, usually symbolized by Land measured in henry His the tendency of a circuit to oppose any changes in the current.

This opposition to a change in the current shows up as a slowing of the rise or fall of the current in circuits. Inductance is a property of electrical devices. Devices having this property are called inductors.

The inductance of a device, like resistance and capacitance, depends on geometrical factors like the size of the device and on the material from which the device is made. It does not depend on the current in the device. Consider a simple circuit consisting of a switch, a resistor Rand a battery. Checkpoint 1: Ask your TA to check your connections before proceeding.

### General Physics Experiment 7

Checkpoint 2: Ask your TA to check your data and calculations. Checkpoint 3: Ask your TA to check your data, Excel graph, and calculations. Checkpoint 4: Ask your TA to check your data, Excel graph, and calculations.The oscilloscope was connected to the inductor. The input voltage was maintaining at 4V. The voltage across the inductor was measured in different values of frequency table 1.

Then the resistor interchanges position with the inductor. The voltage across the resistor was measured and the current of the circuit was calculated in different values of frequency table 1. The voltage from one side of coil to the other side will rise with frequency since the inductive reactance increases directly with frequency and the impedance of the resistor is essentially independent of the applied frequency.

The shapes of the curves versus frequency will have the same characteristics since the voltage and current of the resistor are related by the fixed resistance value. At very low frequency the inductive reactance will be small compared to the series resistive element and the network will be primarily resistive in nature.

The phase angle associated with the input impedance approaching 0 fates. At increasing frequencies XL will drown out the resistive element and the network will be primarily inductive, resulting in an input phase angle approaching 90 fates.

On the table 1 seeing that as the frequency increases the voltage across the inductor increases but the voltage across the resistor and the current decreases.

On the table 2 seeing that as the frequency increases the ZT increases. There is same difference between the two different formulas of ZT. On the table 2 seeing that there is a small difference between the two formulas of ZT. Site map Print RSS. Make a free website Webnode.

## Analyzing the Response of an RLC Circuit

Vasilis Leandrou Engineer. Search site. Frequency Response of R-L network. Website powered by Webnode Launch your own website for free!

V L p-p. V R p-p. I p-p. E p-p.Ideal and Real Inductors and Capacitors. In measuring inductance values, it will be found that real components are not ideal.

Thus, the impedance of the device is represented by either a series or a parallel equivalent as shown in the figure at the left. Conventionally, real capacitors are represented by a parallel circuit of a perfect capacitor and resistor while real inductors are represented by a series circuit of a perfect inductor and a resistor. A simple LCR meter just gives an estimate of the total impedance converted into Farads or Henrys for capacitors and inductors, respectively, and does not give you any information about the resistive parts.

The impedance bridge does provide this additional information for the components at a particular frequency, usually 1 kHz and these are given in the form of dissipation and quality factors.

The impedance, and hence the response, of any circuit containing reactive elements depends upon frequency. Thus any circuit containing reactive elements can be called a frequency selective circuitsince it provides a certain response to certain frequencies. However, the term is usually used to denote only a circuit specifically designed to separate different frequencies. This is the function of RLC series and parallel circuits, which are "resonant" at a specific frequency.

Series RLC Circuits:. A series circuit containing R, L, and C is in resonance when the current in the circuit is in phase with the total voltage across the circuit. Depending on the particular values of R, L, and C, resonance occurs at one distinct frequency. Because of its distinct frequency characteristics, the series resonant circuit is one of the most important frequency selective circuits.

An important consideration when designing an RLC circuit is the nonideal nature of the reactive components. Real capacitors closely approximate perfect capacitors so we may neglect the parallel resistance associated with D.

Real inductors, however, have a small series resistance which is shown in the circuit diagram as r. This cannot normally be neglected since the Q of real inductors is not infinitely large. However, the approximation is fairly good and measured transfer functions do not differ much from it for reasonable ranges of frequency.

F has both a phase and a magnitude as a function of frequency. The graph below shows a series of plots of the transfer function for a series RLC circuit where the inductance had a value of 1. As you can see, the highest Q circuit had the least loss and the narrowest passband. The passband is defined as the difference, in Hz, between the two frequencies at which the F is down 3 dB from its peak value.Impedance Measurement. Use an impedance bridge to measure the capacitance and dissipation factor D for the capacitors at Hz and the quality factor Q for the inductors on your component board.

Measure the Q of the inductors at the both of the two frequency options provided on the instrument. Typically a 1kHz test signal is used to measure inductors that are used in audio and RF radio frequency circuits.

This is because these components operate at higher frequencies and require that they be measured at a higher frequency of 1kHz. However, a Hz test signal is used to measure inductors that are used as filter chokes in power supplies that typically operate at 60 Hz AC with Hz filter frequencies.

Connect a series RLC circuit using one of the smaller inductors and one of the capacitors you measured in the lab. Use a resistance box to provide a value of 50 ohms for R. The resistance marked ' r ' is the series resistance associated with the inductor. Calculate the expected resonant frequency.

Use a resistor decade box or substituion box to provide the resistance, R. Model the circuit from Hz to 1 GHz. A parallel RLC circuit is commonly used as a bandstop filter, because here the voltage and current across the output resistor, R1, is at a minimum at resonance.

Use a resistor decade box or substitution box to provide the resistance, R. The properties of the series and parallel circuit can be combined to accentuate one signal and reject another.The objective of this lab activity is to study the phenomenon of resonance in RLC circuits.

Determine the resonant frequency and bandwidth of the given network using the amplitude response to a sinusoidal source. A resonant circuit, also called a tuned circuit, consists of an inductor and a capacitor together with a voltage or current source.

It is one of the most important circuits used in electronics. For example, a resonant circuit, in one of many forms, allows us to tune into a desired radio or television station from the vast number of signals that are around us at any time.

**LCR**

A network is in resonance when the voltage and current at the network input terminals are in phase and the input impedance of the network is purely resistive. Consider the parallel RLC circuit of Figure 2. The steady-state admittance offered by the circuit is:. Resonance occurs when the voltage and current at the input terminals are in phase. This corresponds to a purely real admittance, so that the necessary condition is given by.

Frequency response is a plot of the magnitude of the output voltage of a resonance circuit as a function of frequency. The frequency response is shown in Figure 3. You can find the answers at the StudentZone blog.

As in all the ALM labs, we use the following terminology when referring to the connections to the ALM connector and configuring the hardware. When a channel is configured in the high impedance mode to only measure voltage, —H is added as in CA-H.

File: alice-desktop Please download here. For more information, please look here. Doug Mercer received his B. Since joining Analog Devices inhe has contributed directly or indirectly to more than 30 data converter products and he holds 13 patents.

He was appointed to the position of ADI Fellow in He is currently an M. JUL Doug Mercer Doug Mercer received his B.Objective: 1. Compare measured and calculated voltages and current for a series - parallel RLC circuit at discrete frequencies. Measure voltage amplitude and phase. Measure current amplitude and phase indirect. Use PSpice to simulate and analyze a series - parallel RLC circuit at discrete frequencies and over a wide range of frequencies. By inspection, estimate Vo for: a.

Use PSpice to plot Vo vs. AC analysis. These calculations were performed in several steps starting with the following. In determining the circuits overall and piece wise components the individual and total impedance was calculated for each component of the circuit see Table 1 using the following equations. Several properties of Pspice were used including that of the transient analysis.

By using the. TRAN analysis statement Pspice incorporates a very detailed differential equation solver routine that may cause initial problems within a circuit using time dependent components such as capacitors and inductors.

As found the capacitors and inductor had an initial effect on the circuit at time equal to zero. Thus requiring several hand calculations to determine the effects of each time dependent component when time is set equal to zero see Table 3.

To solve for these initial conditions the follow equations were used. With close inspection of equations E. Although upon closer examination the values of the current and voltages effecting the time dependent components were originally calculated based upon the specific frequency of either 1kHz or 10kHz. The input sine wave was set using a function generator at 1kHz, 10kHz and a 4volt peek waveform. The input signals frequency and voltage were then confirmed with the use of an oscilloscope.

Measured data was then taken with respect to the variables Vo, I 1I 2I 3 for both frequencies. Measuring Vo was a direct measurement although for the currents required an indirect approach. By measuring the voltage across R 1R 2R 3 and applying ohms law E.Fig 2. The phase angle in each of the above expressions and in the phasor diagram Fig 2 indicates that:. Voltages can be measured or calculated by multiplying current and the impedance across each component.

User Tools Login. Site Tools. Table of Contents General Physics Experiment 7. Resistor Inductor Capacitor Series Circuits. To observe the relationships between the voltage and current across resistors, inductors, and capacitors in series combinations as the frequency of the source is varied. Figure 1 Figure 2. You can see that impedance for a resistor is simply its resistance, however the other components are more complicated.

Impedance for a capacitor varies inversely with the capacitance and angular frequency. This means when we have a large angular frequency impedance will be very small, conversely for a very small angular frequency impedance will be large. Since impedance varies proportionally with angular frequency, a large frequency translates into a large impedance and a small frequency would result in a small impedance. Make certain that the red probe wire of each voltage sensor is connected at the higher voltage side of each element.

Figure 3 and video.

### Series RLC Circuit: Analysis & Example Problems

The amplitude should be set to 4 V and the frequency will be adjusted as needed so keep this dialog box readily available. Adjust the frequency on the signal generator to 10 Hz and click the Start button to collect data. Rescale the graph using the icon at the upper left and zoom as needed. The most effective way to zoom is to grab one of the numbers along the x-axis and slide right or left. After collecting data for each frequency, clear the screen by clicking Experiment, Delete All Data Runs.

Enter your maximum voltage values and frequencies from table 1 All 5 columns of table 1. The ratio of the inductor voltage to the resistor voltage is found from Eqs. The ratio of capacitor voltage to resistor voltage is found from Eqs. If the D2L site is down, email.

Methods Used: Insert a labeled webcam image of apparatus. Describe what and how measurements are made.

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