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RLC Circuits Questions and Answers for Viva

RLC Circuits Viva Interview Questions with Answers

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Interview Question and Answer of RLC Circuits

Question-1. What is an LRC circuit?

Answer-1: An LRC circuit is a type of electrical circuit that consists of an inductor (L), a resistor (R), and a capacitor (C) connected in series or parallel.

Question-2. What is the difference between series and parallel LRC circuits.

Answer-2: In a series LRC circuit, the components are connected sequentially, while in a parallel LRC circuit, the components are connected across the same voltage source.

Question-3. What is the behavior of an LRC circuit at resonance?

Answer-3: At resonance, the capacitive reactance and the inductive reactance cancel each other out, resulting in maximum current flow and minimum impedance.

Question-4. How does the behavior of a series LRC circuit differ from that of a parallel LRC circuit at resonanc

Answer-4: In a series LRC circuit, the current is maximum and the impedance is minimum at resonance, whereas in a parallel LRC circuit, the voltage across the circuit is maximum at resonance.

Question-5. What is the resonance frequency of an LRC circuit?

Answer-5: The resonance frequency (f_res) of an LRC circuit is given by the formula: f_res = 1 / (2π√(LC)), where L is the inductance and C is the capacitance.

Question-6. Define the quality factor (Q) of an LRC circuit.

Answer-6: The quality factor (Q) of an LRC circuit measures the selectivity or sharpness of resonance and is given by the ratio of the reactance to the resistance at resonance.

Question-7. How does the Q factor affect the bandwidth of an LRC circuit?

Answer-7: A higher Q factor results in a narrower bandwidth and a sharper resonance peak, indicating better selectivity.

Question-8. Explain the transient behavior of an LRC circuit.

Answer-8: During transient behavior, the currents and voltages in the circuit change over time in response to sudden changes in input, such as switching on or off.

Question-9. What is the time constant of an LRC circuit?

Answer-9: The time constant (𝜏) of an LRC circuit is given by the formula: 𝜏 = L / R, where L is the inductance and R is the resistance.

Question-10. How does the energy storage in an LRC circuit change with frequency?

Answer-10: At resonance, the energy is primarily stored in the magnetic field of the inductor and the electric field of the capacitor. At other frequencies, energy storage varies between the inductor and capacitor depending on reactance.

Question-11. What is the significance of damping in an LRC circuit.

Answer-11: Damping determines how quickly the oscillations in the circuit decay over time. Overdamped circuits have slow decay, underdamped circuits have oscillations, and critically damped circuits decay as quickly as possible without oscillation.

Question-12. What happens to the phase difference between voltage and current in an LRC circuit at resonance?

Answer-12: At resonance, the phase difference between voltage and current is zero, indicating that they are in phase.

Question-13. Describe the transfer function of an LRC circuit.

Answer-13: The transfer function of an LRC circuit relates the output voltage to the input voltage and is influenced by the values of resistance, inductance, and capacitance in the circuit.

Question-14. How does the presence of damping affect the natural frequency of an LRC circuit?

Answer-14: Damping reduces the amplitude of oscillations and slightly lowers the natural frequency of the circuit.

Question-15. Explain the role of LRC circuits in bandpass and bandstop filters.

Answer-15: LRC circuits can be configured as bandpass filters, allowing a specific range of frequencies to pass while attenuating others, or as bandstop filters, blocking a specific range of frequencies while passing others.

Question-16. What is the effect of increasing the capacitance in an LRC circuit?

Answer-16: Increasing the capacitance decreases the resonance frequency and widens the bandwidth of the circuit.

Question-17. What are the applications of LRC circuits in electronics?

Answer-17: LRC circuits are used in various applications such as filters, oscillators, resonant circuits in radio frequency (RF) systems, and power supplies.

Question-18. What is the effect of increasing the capacitance in an LRC circuit?

Answer-18: Increasing the capacitance decreases the resonance frequency and widens the bandwidth of the circuit.

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Frequency response of R-L-C series Circuit            

Introduction.

Series RLC circuits consist of a resistance, a capacitance and an inductance connected in series across an alternating supply. Series RLC circuits are classed as second-order circuits because they contain two energy storage elements, an inductance L and a capacitance C. Consider the RLC circuit below. In this experiment a circuit(Fig 1) will be provided. A p-p sinusoidal signal of amplitude 3V will be applied to it and its frequency response would be verified .

Figure 1:Circuit diagram

The above R, L, C series circuit forms a second order system.The transfer function of this circuit is given by,

$$H(s) = \frac{\frac{1}{LC}}{s^2 + (\frac{R}{L})s + \frac{1}{LC}}$$

can be compared with general equation.

$$H(s) = \frac{\omega_n^2} {s^2 + 2 \zeta \omega_n s + \omega_n^2} \ where \ \omega_n \ = \frac{1}{\sqrt{LC}}$$

The gain and phase response against frequency will be typical of second order system. The expected maximum gain for each ζ can be observed from the plot in the experiment. Theoretical expression for obtaining maximum gain is,

$$M_m = \frac{1}{2 \omega \sqrt{1 - \zeta^2}}$$

$$Occurring \ at \ \omega_m = \omega_n \sqrt{1 - 2 \zeta^2}$$

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Resonance in Series-Parallel Circuits

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• Alternating Current (AC)

In simple reactive circuits with little or no resistance, the effects of radically altered impedance will manifest at the resonance frequency predicted by the equation given earlier. In a parallel (tank) LC circuit, this means infinite impedance at resonance. In a series LC circuit, it means zero impedance at resonance:

However, as soon as significant levels of resistance are introduced into most LC circuits, this simple calculation for resonance becomes invalid.

On this page, we’ll take a look at several LC circuits with added resistance , using the same values for capacitance and inductance as before: 10 µF and 100 mH, respectively.

Calculating the Resonant Frequency of a High-Resistance Circuit

According to our simple equation above, the resonant frequency should be 159.155 Hz. Watch, though, where current reaches maximum or minimum in the following SPICE analyses:

Parallel LC circuit with resistance in series with L.

Resistance in series with L produces minimum current at 136.8 Hz instead of calculated 159.2 Hz

Parallel LC with resistance in serieis with C.

Here, an extra resistor (Rbogus) is necessary to prevent SPICE from encountering trouble in analysis. SPICE can’t handle an inductor connected directly in parallel with any voltage source or any other inductor, so the addition of a series resistor is necessary to “break up” the voltage source/inductor loop that would otherwise be formed.

This resistor is chosen to be a very low value for minimum impact on the circuit’s behavior.

Resistance in series with C shifts minimum current from calculated 159.2 Hz to roughly 180 Hz.

Series LC Circuits

Switching our attention to series LC circuits, we experiment with placing significant resistances in parallel with either L or C. In the following series circuit examples, a 1 Ω resistor (R1) is placed in series with the inductor and capacitor to limit total current at resonance.

The “extra” resistance inserted to influence resonant frequency effects is the 100 Ω resistor, R2. The results are shown in the figure below.

Series LC resonant circuit with resistance in parallel with L.

Series resonant circuit with resistance in parallel with L shifts maximum current from 159.2 Hz to roughly 180 Hz.

And finally, a series LC circuit with the significant resistance in parallel with the capacitor The shifted resonance is shown below.

Series LC resonant circuit with resistance in parallel with C.

Resistance in parallel with C in series resonant circuit shifts current maximum from calculated 159.2 Hz to about 136.8 Hz.

Antiresonance in LC Circuits

The tendency for added resistance to skew the point at which impedance reaches a maximum or minimum in an LC circuit is called antiresonance . The astute observer will notice a pattern between the four SPICE examples given above, in terms of how resistance affects the resonant peak of a circuit:

Parallel (“tank”) LC circuit:

• R in series with L: resonant frequency shifted down
• R in series with C: resonant frequency shifted up

Series LC circuit:

• R in parallel with L: resonant frequency shifted up
• R in parallel with C: resonant frequency shifted down

Again, this illustrates the complementary nature of capacitors and inductors : how resistance in series with one creates an antiresonance effect equivalent to resistance in parallel with the other. If you look even closer to the four SPICE examples given, you’ll see that the frequencies are shifted by the same amount , and that the shape of the complementary graphs are mirror-images of each other!

Antiresonance is an effect that resonant circuit designers must be aware of. The equations for determining antiresonance “shift” are complex, and will not be covered in this brief lesson. It should suffice the beginning student of electronics to understand that the effect exists, and what its general tendencies are.

The Skin Effect

Added resistance in an LC circuit is no academic matter. While it is possible to manufacture capacitors with negligible unwanted resistances, inductors are typically plagued with substantial amounts of resistance due to the long lengths of wire used in their construction.

What is more, the resistance of wire tends to increase as frequency goes up, due to a strange phenomenon known as the skin effect where AC current tends to be excluded from travel through the very center of a wire, thereby reducing the wire’s effective cross-sectional area.

Thus, inductors not only have resistance, but changing, frequency-dependent resistance at that.

Added Resistance in Circuits

As if the resistance of an inductor’s wire weren’t enough to cause problems, we also have to contend with the “core losses” of iron-core inductors, which manifest themselves as added resistance in the circuit.

Since iron is a conductor of electricity as well as a conductor of magnetic flux, changing flux produced by alternating current through the coil will tend to induce electric currents in the core itself ( eddy currents ).

This effect can be thought of as though the iron core of the transformer were a sort of secondary transformer coil powering a resistive load: the less-than-perfect conductivity of the iron metal. This effects can be minimized with laminated cores, good core design high-grade materials, but never completely eliminated.

RLC Circuits

One notable exception to the rule of circuit resistance causing a resonant frequency shift is the case of series resistor-inductor-capacitor (“RLC”) circuits. So long as all components are connected in series with each other, the resonant frequency of the circuit will be unaffected by the resistance. The resulting plot is shown below.

Series LC with resistance in series.

Resistance in series resonant circuit leaves current maximum at calculated 159.2 Hz, broadening the curve.

Note that the peak of the current graph has not changed from the earlier series LC circuit (the one with the 1 Ω token resistance in it), even though the resistance is now 100 times greater. The only thing that has changed is the “sharpness” of the curve.

Obviously, this circuit does not resonate as strongly as one with less series resistance (it is said to be “less selective”), but at least it has the same natural frequency!

Antiresonance’s Dampening Effect

It is noteworthy that antiresonance has the effect of dampening the oscillations of free-running LC circuits such as tank circuits. In the beginning of this chapter we saw how a capacitor and inductor connected directly together would act something like a pendulum, exchanging voltage and current peaks just like a pendulum exchanges kinetic and potential energy.

In a perfect tank circuit (no resistance), this oscillation would continue forever, just as a frictionless pendulum would continue to swing at its resonant frequency forever. But frictionless machines are difficult to find in the real world, and so are lossless tank circuits.

Energy lost through resistance (or inductor core losses or radiated electromagnetic waves or . . .) in a tank circuit will cause the oscillations to decay in amplitude until they are no more. If enough energy losses are present in a tank circuit, it will fail to resonate at all.

Antiresonance’s dampening effect is more than just a curiosity: it can be used quite effectively to eliminate unwanted oscillations in circuits containing stray inductances and/or capacitances, as almost all circuits do. Take note of the following L/R time delay circuit: (Figure below)

L/R time delay circuit

The idea of this circuit is simple: to “charge” the inductor when the switch is closed. The rate of inductor charging will be set by the ratio L/R, which is the time constant of the circuit in seconds.

However, if you were to build such a circuit, you might find unexpected oscillations (AC) of voltage across the inductor when the switch is closed. (Figure below) Why is this? There’s no capacitor in the circuit, so how can we have resonant oscillation with just an inductor, resistor, and battery?

Inductor ringing due to resonance with stray capacitance.

All inductors contain a certain amount of stray capacitance due to turn-to-turn and turn-to-core insulation gaps. Also, the placement of circuit conductors may create stray capacitance. While clean circuit layout is important in eliminating much of this stray capacitance, there will always be some that you cannot eliminate.

If this causes resonant problems (unwanted AC oscillations), added resistance may be a way to combat it. If resistor R is large enough, it will cause a condition of antiresonance, dissipating enough energy to prohibit the inductance and stray capacitance from sustaining oscillations for very long.

Interestingly enough, the principle of employing resistance to eliminate unwanted resonance is one frequently used in the design of mechanical systems, where any moving object with mass is a potential resonator.

A very common application of this is the use of shock absorbers in automobiles. Without shock absorbers, cars would bounce wildly at their resonant frequency after hitting any bump in the road. The shock absorber’s job is to introduce a strong antiresonant effect by dissipating energy hydraulically (in the same way that a resistor dissipates energy electrically).

• Added resistance to an LC circuit can cause a condition known as antiresonance , where the peak impedance effects happen at frequencies other than that which gives equal capacitive and inductive reactances.
• Resistance inherent in real-world inductors can contribute greatly to conditions of antiresonance. One source of such resistance is the skin effect , caused by the exclusion of AC current from the center of conductors. Another source is that of core losses in iron-core inductors.
• In a simple series LC circuit containing resistance (an “RLC” circuit), resistance does not produce antiresonance. Resonance still occurs when capacitive and inductive reactances are equal.

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Resonance in Series and Parallel RLC Circuit | Resonance Frequency

This article examines the resonance phenomenon and resonance frequency in series and parallel rlc circuits, along with several examples. .

In any AC circuit consisting of resistors, capacitors, and inductors, either in series or in parallel, a condition can happen in which the reactive power of the capacitors and of the inductors become equal. This condition is called resonance .

Simultaneous with the capacitive reactive power and the inductive reactive power being equal, other features can reflect resonance. Remember that we always reduce a circuit to a single resistor, a capacitor, and an inductor. Thus, for this discussion, we assume one of each component in the circuit.

Resonance: a Special condition in AC circuits where all the energy stored by inductive components is provided by capacitive components, and vice versa. This occurs in a particular frequency. This condition implies other facts such as:

• The net reactive power to be zero,
• The power factor to be unity, and

In fact, when resonance happens, the inductive reactance and the capacitive reactance are equal to each other:

$\begin{matrix}   {{X}_{L}}={{X}_{C}} & {} & \left( 1 \right)  \\\end{matrix}$

Figure 1. Resonance condition in Series and Parallel AC circuits.

In a circuit with a fixed frequency, resonance can happen if the condition in  Equation 1  is true.

 On the other hand, since both  X L  and  X C  are functions of frequency, if the frequency of a circuit changes, at a unique frequency these values can become equal. 

Figure 1  shows the variation of the impedance for the three basic types of loads in a circuit versus frequency. The horizontal axis implies a frequency increase.

 A resistor is independent of frequency; thus, its impedance is constant, represented by a line parallel to the horizontal axis. The impedance of an inductor is proportional to the frequency and augments as the frequency increases. For a capacitor the reverse happens and its impedance decreases (though not linearly) as the frequency increases.

At the point of intersection of the two curves,  X L  = X C,  and the frequency at that point is called the  resonant frequency  or  resonance frequency  and is denoted by  f R .

Resonant frequency:  A unique frequency for each AC circuit containing both reactive components (inductors and capacitors) at which the resultant reactance of all capacitive components is equal to the resultant reactance of all the inductive components. As a result, the two types of components cancel the effect of each other, and the total reactive power of the circuit is zero.

Resonance frequency:  Frequency at which resonance happens in an AC circuit.

The resonance frequency can be found by equating X L  and  X C . This leads to

\[\begin{matrix}   {{f}_{R}}=\frac{1}{2\pi \sqrt{LC}} & {} & \left( 2 \right)  \\\end{matrix}\]

Resonance Frequency Calculation Example 1

Find the resonance frequency of a 40 mH inductor and a 51 μF capacitor.

Values of the capacitance and inductance in Farad and Henry can directly be plugged in  Equation 2 . Thus,

\[{{f}_{R}}=\frac{1}{2\pi \sqrt{LC}}=\frac{1}{2\pi \sqrt{0.040*0.00051}}=112Hz\]

Resonance Frequency Calculation Example 2

Find the capacitance for a capacitor to become in resonance with a 40 mH inductor at 60 Hz frequency.

At 60 Hz the reactance of the capacitor must be the same as the reactance of the inductor. Thus,

$\begin{align}  & {{X}_{C}}={{X}_{L}}=2\pi *60*0.040=15\Omega  \\ & C=\frac{1}{2\pi *60*15}=176mF \\\end{align}$

Note that if this value is not among the standard values for capacitors, one can make such a value by combining a number of standard capacitors in series and/or parallel.

Resonance in Series RLC Circuits

When resonance occurs in a series  RLC  circuit , the resonance condition ( Equation 1 ) leads to other relationships or properties. These are

• The voltage across the inductor is equal to the voltage across the capacitor.
• The voltage across the resistor is equal to the applied voltage.
• The impedance of the circuit has its lowest value and is equal to  R .
• Circuit current assumes its maximum value because the impedance is minimum.
• The power factor for the circuit becomes equal to 1, and the phase angle is zero.
• Apparent power has its lowest value and becomes equal to the active power because the power factor is 1.

Resonance in Parallel RLC Circuits

Similar to the series circuits, when resonance occurs in a parallel  RLC  circuit the resonance condition ( Equation 1 ) leads to other relationships or properties:

• The current in the inductor is equal to the current in the capacitor.
• The current in the resistor is equal to the total circuit current.
• The impedance of the circuit has its highest value and is equal to  R .
• Circuit current assumes its minimum value because the impedance has the highest value.

Items 5 and 6 are the same as for the series resonant circuits, but the rest are quite different.

Figure 2.  Principle of induction heater and induction cooker.

When resonance occurs in a parallel  RLC  circuit, a local current circulates between the inductor and the capacitor. This current can be very high, while the circuit current as seen from the source can be low. This phenomenon is used in induction heaters (in the industry for heating metals when necessary, e.g., heating bearings for mounting or dismounting) and in induction cookers (for domestic use).

In such an application a high current is flowing through an inductor, whereas the current provided by the power line is small. This means that the rating of the wires and breakers is much smaller than the current in the inductor.

The current in the inductor creates (induces) local currents in the piece to be warmed, without even touching it. In the case of an induction cooker, the body of the cooking pan becomes hot owing to local currents created by induction. This is shown in  Figure 2 .

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• determination of the equivalent resistance of two resistors when connected in series and parallel viva questions
• Determination of the Equivalent Resistance of Two Resistors When Connected in Series and Parallel

1) What are the materials required for part (a) of this experiment?

A battery, a plug key, connecting wires, an ammeter, a voltmeter, a rheostat, a piece of sandpaper and two resistors of varied values are the materials required for part (a) of this experiment.

2) What are the materials required for part (b) of this experiment?

Two resistors of varied values, a battery of 6 volts, an ammeter, a plug key, connecting wires, a piece of sandpaper, a voltmeter and a rheostat are the materials required for part (b) of this experiment.

3) What is meant by resistance?

Resistance is the opposition that a material exerts against the flow of current.

4) What is a resistor?

A resistor is a passive electrical device that provides electrical resistance in an electrical circuit. A resistor is used to decrease the flow of current, regulate signal levels, bias active components, etc.

5) What is meant by the electrical current?

An electric current is the flow of charged particles such as ions or electrons. They typically move through a space or an electric conductor.

6) What is an ammeter?

An ammeter is an electrical instrument used for measuring either alternating or direct electrical current.

7) What is a voltmeter?

A voltmeter is an electrical instrument used for calculating the electric potential difference across two points in a circuit.

8) What are the two fundamental types of resistors?

Linear resistors and variable resistors are the two fundamental types of resistors.

9) What are the main types of variable resistors?

Potentiometer, thermostat, and trimmer resistor are the main types of variable resistors.

10) What is a rheostat?

A rheostat is a type of variable resistor which is mainly used to regulate current. It is able to change the resistance without interruption.

11) What are the ways through which resistors are connected in an electric circuit?

Resistors are connected in series, parallel or a combination of series and parallel connections.

12) When resistors are connected in parallel, what would be the nature of the total resistance?

The total resistance will be comparatively less when resistors are connected in parallel.

13) When resistors are joined in parallel, what quantities stay constant in the electrical circuit?

When resistors are connected in parallel, the current does not remain constant, but the potential difference remains constant.

14) What is the commonly used type of connection applied while wiring a house?

Typically, the connections of every circuit in a conventional house are always in parallel.

15) What is the quantity that stays constant in a parallel connection?

Voltage stays the same in a parallel connection.

16) How do you measure the total resistance when three electrical resistors are combined in parallel?

Total resistance Rp can be calculated using the following formula:

1/Rp = 1/R1 + 1/R2 + 1/R3

17) What is the ideal connection orientation for household appliances?

Household electrical appliances should be linked in parallel to provide equal voltage for every appliance.

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Microwave Engineering Questions and Answers – Series and Parallel Resonant Circuits

This set of Microwave Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Series and Parallel Resonant Circuits”.

Sanfoundry Global Education & Learning Series – Microwave Engineering. To practice all areas of Microwave Engineering, here is complete set of 1000+ Multiple Choice Questions and Answers .

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