The Resonant Frequency of a Circuit : Review

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Table of Contents

Introduction
Voltage across the Resistor
Calculations
Open loop gain
Closed loop
Conclusion
Reference List

Introduction

Electrical engineering has caused tremendous changes in the electrical and electronic world. This is due to intensive and frequent researches and discoveries being made by scientists. This has led to electrical and electronic devices which have encompassed a high level of technology thus, enhancing efficiency and effectiveness of these electrical machines.

Voltage across the Resistor

Voltage across the Inductor

These superconductors will be compatible with other electrical devices such transformers, transmission cables and power limiters. For example; a current limiter with a capacity of 10.5 kilovolts and 200 amperes are being tested in some of the power research centres. The need for high-temperature superconductors has been created by the ever increasing number of power consumers. Such innovated superconductors will have the capacity to withstand high-voltage from power generators. Through this, China will have the capacity to supply electricity to major factories and to domestic consumers (Andersen, 2001).

Electrical transformers have undergone tremendous changes through innovation in electric related matters. For instance, a high-voltage power holding 3-phase transformer which can withstand a capacity of 630 kV/10.5 kV for high use have been developed in Japan. Such transformers contain iron core solenoid and other high-voltage resistant materials such as stainless steel. These stainless steel materials get enforced by silver materials coated by polyamide films. This combination has allowed generation of modern electrical transformers which can withstand high electric voltage as well resistance to high temperatures.

In China, modern electric transformers which have an automatic and modern cooling system have been developed. These transformers have replaced the old antiquated transformer which used circulating cooling oil in small metallic pipes. Through this, the conduction of electricity has been necessitated as a high level of degree Celsius can be lowered within a very short time. The inductor that is used is shown below;

Induced electric fields

The first move is to identify a conductor which must be moved in a magnetic field to start off the basic energy transfer. When the movement across the magnetic field takes place, a motional emf arises. This is because of the magnetic force that applies itself on the now mobile charges. The mobile charges always move together with the conductor and for this reason they have a velocity of a nonzero on the average. Moreover it is necessary to have a complete circuit since this will act as the platform around which the charges revolve. For these charges to begin their movements, the magnetic field is the source of their force and spurs them to motion.

Calculations

Suppose an RLC circuit is connected to an ac source with a fixed amplitude but variable frequency like the one given. The impedance depends on frequency. At extreme frequencies, either high or low, the impedance is larger and the amplitude of the current is therefore small.

Resonant frequency

RF=1√Lc =1√0.40*100/rms=0.158 rads/s

Inductive and capacitative reactance at resonance

Xc=1/(wC)

Xc=1/ (0.158*100)

X=15.81 kΩ

The impedance of the circuit is

Z= =

Z=250.02

RMS current at Resonance:

1rms= έ_rms/Z =0.158/250.02 mA. =0.0632 mA.

RMS Voltage across each element at resonance:

V_L-rms=1_rmsX_L=0.0632 mA× 15.81× 10³Ω=32.1222mV

V_c-rms=_{1 rms}X_c=0.0632mA × 15.18 × 10^3Ω=32.1222mV

V_R-rms=1 _rmsR=0.0632mA × 15.18Ω=0.959376mV.

Open loop gain

Open loop gain is a kind of gain which is often used with an Operational amplifier, commonly abbreviated as op-amp.

This benefit is the benefit experienced when nowhere in the circuit the feedback has been utilized

In its traditional form, the open loop gain is overwhelmingly high; to exercise precision, a typical operational amplifier has endless or innumerable or outstanding open-loop gain. This outstanding open-loop gain may stretch up to as far as around 10⁵.

In normal circumstances, feedback serves a particular useful purpose

The reason behind is that the benefit of the whole circuit has to be determined the b kept within certain parameters that facilitate best usage.

This is why the feed back should be applied round the operating system. But to achieve the performance that is necessary fairly considerable heights or levels of feedback is needed. This is however enabled by the favourable high gain of the op-amp.

AOL = Vout/ (V+ – V-)

The definition above V+=V-, is for the suitable amplifier of the open loop gain at infinity.

The above has so far involved the transfer of voltage across certain obstacles. It is important, however to get to know how the voltage or currency applies to motion.

This is by no other means by induction. However, for induction to occur, formation of magnetic fields must be realized.

Closed loop

V=100+ 0.8/100 (R_eq=∑R1=R₁+R₂+…+R_N

V=+ 8/100

0.96=0.08

0.96v-0.008

0.952v.

Conclusion

It is important to note that the resonant frequency of a circuit depends only on the values of the inductance and the capacitance, not on the resistance.

There are moments when the impedance can equal the resistance. This happens at the resonant frequency.

Finally, if the phases were given, the voltages across the inductor and across the capacitor are equal at resonance, but the instantaneous voltages are opposite in phase.

Reference List

Andersen, B., 2001. Technological Change and the Evolution of Corporate Innovation: The Structure of Patenting. Northampton, UK: Edward Elgar Publishing.

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