## Friday, 6 January 2012

### Circuit Theory two mark questions with answer

Department of Electrical and Electronics Engineering.
Electric Circuits
UNIT 1 (Basic Circuit concepts)

1. What do you mean by an electric network and an electric circuit
Interconnection of two or more simple circuit elements (voltage sources, resistors, inductors and capacitors) is called an electric network. If a network contains at least one closed path, it is called an electric circuit.

1. Classify the network elements
i)                    Active or passive
ii)                  Unilateral or bilateral
iii)                Linear or non linear
iv)                Lumped or distributed

1. Differentiate active and passive elements
Energy sources (voltage or current sources) are active elements, capable of delivering power to some external device. The passive elements are those which are capable only of receiving power.

1. Differentiate bilateral and unilateral elements
In the bilateral element, the voltage - current relation is the same for current flowing in either direction. In contrast, a unilateral element has different relations between voltage and current for the two possible directions of current.

1. Differentiate linear and nonlinear elements
An element is said to be linear, if it satisfies the linear voltage current relationship. That means the current through the element is multiplied by some constant ‘α’, and results in the multiplication of voltage across the element by the same constant.
An element which does not satisfy this relation is called a nonlinear element.

1. Define lumped and distributed elements in electric circuits
The elements which are separated physically are known as lumped elements, like resistors, capacitors and inductors. Distributed elements, on the other hand, are those which are not separable for analytical purposes.

1. Write the equations of energy stored by an inductor and capacitor
Energy stored by an inductor is,
W = LI2 / 2
I à Current flow through the inductor

Energy stored by a capacitor
W = CV2 / 2
V à Voltage across capacitor

1. State Kirchhoff’s voltage and current law
Kirchhoff’s voltage law:
It states that the algebraic sum of voltages around any closed path in a circuit is always zero.
Kirchhoff’s current law:
It states that the sum of currents entering into any point is equal to the sum of the currents leaving that point.

1. Write the equation for voltage for the given circuit using voltage division technique

1. Write the equation for current for the given circuit using current division technique

1. How can a practical voltage source, having an ideal voltage VS and internal series resistance RV be replaced by a current source?
The practical voltage source, having an ideal voltage Vs and internal series resistance RV be replaced by a current source I = VS / RV in parallel with an internal resistance       RI = RV

UNIT II   (Sinusoidal steady state analysis)

1. Write the equation for Instantaneous active power, Average power, Apparent power

Instantaneous active power,

P(t) = VmIm[Cos(2ωt+θ)+Cos θ] / 2

Average power,

Pav = VmIm Cos θ / 2

Apparent power,

Papp = Veff Ieff

1. Define Power factor
It is defined as the ratio of average power to the apparent power, whereas the apparent power is the product of the effective values of the current and the voltage.

Power factor = Pav / (Veff Ieff)

It is also defined as the factor with which the volt amperes are to be multiplied to get true power in the circuit

1. Draw the power triangle

1. Give any one application of resonance
In the area of communications, the ability of a radio receiver to select a certain frequency, transmitted by a station and to eliminate frequencies from other stations is based on the principle of resonance.

1. Define resonance frequency for a series RLC circuit

The frequency at which resonance occurs is called the resonant frequency.

fr = 1 / (2π√LC)

L à Inductance of the circuit
C à Capacitance of the circuit

1. Define Bandwidth of a RLC circuit
It is the range of frequencies for which the current or output voltage is equal to 70.7 % of its value at the resonant frequency.

1. Define the Q factor of a RLC series circuit
The Quality factor, Q, is the ratio of the reactive power in the inductor or capacitor to the true power in the resistance in series with the coil or capacitor.

Q = 2π * (maximum energy stored / energy dissipated per cycle)

1. Define Magnification in resonance
The ratio of voltage across either L or C to the voltage applied at resonance can be defined as magnification.

Magnification = (VL / V) or (VC / V)

1. What is tank circuit?
The parallel resonant circuit is generally called a tank circuit, because of the fact that, the circuit stores energy in the magnetic field of the coil and in the electric field of the capacitor. The stored energy is transferred back and forth between the capacitor and coil, and vice-versa.

1. Write the types of balanced and unbalanced loads in a three phase system?

ii)                  Unbalanced three wire star connected load
iii)                Unbalanced four wire star connected load

1. The neutral point of an unbalanced three wire star connected load is called as a floating neutral point. Why?
The potential of the load star point is different from that of the supply star point. The result is that the load phase voltages are not equal to the supply phase voltage and they are not only unequal in magnitude, but also subtend angles other than 120o with one another. The magnitude of each phase voltages depends upon the individual phase loads. The potential of the load neutral point changes according to changes in the impedances of the phases, that is why sometimes the load neutral is also called floating neutral point.

1. When the wattmeter will give down scale reading? How to measure the power under such condition?
If the phase angle between the line voltage and current is greater than 90o, the corresponding wattmeter would indicate downscale reading. To obtain upscale reading, the connections of either the current coil or the pressure coil have to be interchanged. Reading obtained after reversal of coil connection should be taken as negative. Then, the algebraic sum of the two wattmeter readings gives the total power.

Unit – III (Circuits and theorems)

1.                  What do you mean by a planar and a non planar circuit?
A circuit is said to be planar, if it can be drawn on a plane surface without crossovers. A non planar circuit cannot be drawn on a plane surface without a crossover.

2.                  State Superposition theorem
It states that in any linear network containing two or more sources, the response in any element is equal to the algebraic sum of the responses caused by individual sources acting alone, while the other sources are non operative; that is, while considering the effect of individual sources, other ideal voltage sources and ideal current sources in the network are replaced by short circuit and open circuit across their terminals. This theorem is valid only for linear systems.

The Superposition theorem is not valid for power responses. It is applicable only for computing voltage and current responses.

3.                  State Thevenin’s theorem
It states that any circuit having a number of voltage sources, resistances (impedances) and open output terminals can be replaced by a simple equivalent circuit consisting of a single voltage source in series with a resistance (impedances), where the value of the voltage source is equal to the open circuit voltage across the output terminals, and resistance (impedance) is equal to the resistance seen in to the network across the output terminals.

4.                  State Norton’s theorem
It states that any circuit with voltage sources, resistances (impedances) and open output terminals can be replaced by a single current source in parallel with single resistance (impedance), where the value of current source is equal to the current passing through the short circuit output terminals and the value of the resistance (impedance) is equal to the resistance seen into the output terminals.

5.                  State Reciprocity theorem
According to this theorem, if we apply some input( from either a current source, or a voltage source) to a circuit which consists of resistors, inductors, capacitors and transformers, including coupled circuits, the ratio of response(output) in any element to the input is constant even when the position of input and output terminals are interchanged. This is called the Reciprocity theorem.

6.                  State Compensation(Substitution) theorem
It states that any element in the network, linear or non linear, may be replaced by a voltage source of magnitude equal to line current, passing through the element multiplied by the value of the element, provided the currents and voltages in other parts of the circuit remain unaltered.
This theorem is useful to find the changes in current or voltage when the value of resistance is changed in the circuit.

7.                  State Reciprocity theorem
It states that maximum power is delivered from a source to a load when the load resistance is equal to the source resistance.

8.                  State Millman’s theorem

Unit – IV (Response of Electric Circuits)

1. What is transient state?
If a network contains energy storage elements, with change in excitation, the current and voltages change from one state to other state. The behaviour of the voltage (or) current when it is changed from one state to another state is called transient state.

1. What is natural response?
If a circuit containing storage elements which are independent of sources, the response depends upon the nature of the circuit, it is called natural response.

1. What is meant by natural frequency?
If the damping is made zero then the response oscillates with natural frequency without any opposition, such a frequency is called natural frequency of oscillation, denoted as ωn.

1. Define Damping ratio.
It is the ratio of actual resistance R in the circuit to the critical resistance RC. It is denoted by greek letter zeta ζ.
.

1. Write down few applications of RL, RC and RLC circuits.
The few applications of RL,RC and RLC circuits are given below.
Coupling circuits,
Phase-shift circuits,
Filters,
Resonant circuits,
AC bridge circuits, and
Transformers.

1. What is the time-constant for RL and RC circuits?
Time constant for RL circuit, =L/R
Time constant for RC circuit, =1/RC

1. How does an inductor act at t=0+ and t=∞?
An inductor will act as a open circuit at t=0+ and will act as a short circuit at t=∞.

1. Obtain the natural frequency and time constant of an RLC series circuit with R=1K, L=100mH and C=0.1F.

1. What is meant by over damped and under damped system?

1. When do we get transient response?
Whenever a circuit is switched from one condition to another either by a change in the applied source (or) change in the circuit elements there is a transitional period during which the branch currents and voltage change from their values to new ones, this period is called transient.

1. Distinguish between steady state and transient response of an electric circuit.
 SL.No STEADY STATE RESPONSE TRANSIENT RESPONSE 1 Amplitude will not change. Amplitude may change. 2 Frequency will not change. Frequency may change. 3 Constant voltage and current with time. Change from one steady state to another. 4 Algebraic equations are used. Integro-differential equations are used

1. What are the causes of transient behavior occurring in a circuit?
The causes are
a)      It may be due to the sudden change of applied voltage.
b)      When the voltage source is shorted.
c)      When a circuit is connected or disconnected and
d)     Due to storage elements in the circuit.

1. Define Decrement factor or logarithmic decrement.

1. What is the Laplace transform  ?

1. What is the cause of free response in electric circuits?
The presence of storage element such as inductors or capacitors or both in a network in the absence of external energy source is the cause of free response.

1. Find the poles and zeros for the function , and also obtain the pole-zero plot.

Unit – V (Two port network and Filters)

1. Define one-port network.
A pair of terminals at which a signal may enter (or) leave a terminal is called a port. A network having only one such pair of terminals is called one-port network.

1. Define transmission parameters.

1. Write ABCD parameters in terms of Z-parameters.
ABCD parameters in terms of Z-parameters is given below.

A circuit consisting of constant sources is said to be in steady state if the voltages and currents do not change with time.

1. What is meant by free response?
Free response is due to the internal energy stored in the network. It depends upon the type of elements, their size etc. This response is independent of the source. This  response dies gradually, i.e., it approaches zero as time becomes infinity. Free response is also known as natural (or) transient response.

1. Distinguish between free and forced response.
When a circuit contains storage elements which are independent of the sources, the response depends upon the nature of circuit. This response is called natural (or) free response.
The storage elements deliver the energy to the resistances. So the response changes with time, gets saturated after some time. It is referred to as the transient response. When we consider sources acting on a circuit, the response depends on the nature of such sources. This response is called forced response.

10. What is a Low pass filter?

11. Draw the characteristics of ideal low pass filter.

12. What is a high pass filter?
A high-pass filter is a filter that passes high frequencies well, but attenuates
(reduces the amplitude of) frequencies lower than the cutoff frequency.

13. Draw a high pass and low pass filter using RC.

14. Give the applications of filter.
High-pass and low-pass filters are also used in digital image processing to perform
transformations in the spatial frequency domain.
Most high-pass filters have zero gain (-inf dB) at DC. Such a high-pass filter with
very low cutoff frequency can be used to block DC from a signal that is undesired
in that signal (and pass nearly everything else). These are sometimes called DC
blocking filters.

1. A constant k high pass filter is required for a cut-off frequency of 2500Hz. The
resistance of load circuit is 600Ω. Determine the value of the components
required.
SOLUTION:

1. Each of the series elements of a T-type Low pass filter consists of an inductance of 30mH having negligible resistance and the shunt element has a capacitance of 0.2µF. Calculate the cut-off frequency and determine the iterative impedance at a frequency of 1000Hz.
GIVEN:
L/2=30mHL=60mH, C=0.2µF

SOLUTION:
CONFIGURATION OF T-SECTION

Iterative impedance (or) Characteristic impedance,