FEE question paper solved section 1 2019

 FUNDAMENTALS OF ELECTRICAL ENGINEERING, 2019 paper solved.

                                                               

 

Q.1 (a) Select the most appropriate option: (Each of one mark)

1. With Ohm's law, if voltage increases and resistance stays the same:

a. Current Remains the Same

b. Power Decreases

c. Current Increases

d. Resistance Decreases

Ans: C

2. KCL is based on the fact that_______.

a. There cannot be an accumulation of charge at a node.

b. There is a possibility for a node to store energy.

c. Charge accumulation is possible at node

d. Charge accumulation may or may not be possible.

Ans :B

3. A battery is made by combination of 6 cells in series, each capable of

delivering 4 ampere at 2V. How much voltage and current can it

deliver?

a. 12V and 24A

b. 2V and 24A

c. 12V and 4A

d. 2V and 4A

Ans:C

4. Capacitance of a parallel plate capacitor decreases by_______.

a. Increasing the area of plates

b. Increasing the distance between the plates

c. Putting a dielectric between the plates

d. Decreasing the distance between the plates

Ans:B

5. The strength of a magnetic field around an infinite current carrying

conductor is_______.

a. Directly proportional to the distance

b. Same every where

c. Inversely proportional to the distance

d. Inversely proportional to the square of the distance

Ans:C

6. M.M.F is analogous to_______.

a. Electric current in electric circuit

b. Current density in conductor

c. Electromotive force

d. Voltage

Ans:C

(b) Answer following questions: (Each of two mark) 10

1. Define following terms:

1) Node 2) Junction

Node : The point through which an circuit element is connected to the circuit is called Node

Here point A,B,C and D is called Node

 Ans:Any point in an electric circuit where two or more conductors are joined together is a junction.

2. Justify the statement: Capacitor can store more energy if the size of

the capacitor plates is larger but the distance between them is

smaller.

Ans : We know,        C=ϵ⋅A/d,

 This relation show that  when the  when the distance between two plate is lesser the capacitance is greater  and  capacitance is directly proportional to area of each plate.

 

3. Draw star-delta configurations. Mention the expressions for star-

delta transformations.

Ans:

 

 

4. Show the application of Kirchoff’s current law in an electrical circuit

with suitable example.

Ans: It states that the sum of the currents flowing towards a junction is equal to the sum of currents leaving the junction.

This is in accordance with the conservation of charge which is the basis of Kirchhoff's current rule.

 

1.The Wheatstone bridge is an essential application of Kirchhoff's laws

 2.It is also used in mesh and node analysis

 

5. Define Permeance.

Ans:  Permeance is defined as a measure of the ease with which  Magnetic Flux can be admitted through a material or Magnetic circuit. Permeance is the reciprocal of reluctance. Permeance is directly proportional to the magnetic flux. Its unit is Wb/AT or Henry.

 

 

Q.2 (a) Define term: Hysteresis. Sketch and explain hysteresis loop in detail. 06

Ans: The meaning of hysteresis is ”lagging”.  Hysteresis is characterized as a lag of magnetic flux density (B) behind the magnetic field strength (H).

 

 

Looking at the graph, if B is measured for various values of H and if the results are plotted in graphic forms then the graph will show a hysteresis loop.

• The magnetic flux density (B)  is increased when the magnetic field strength(H) is increased from 0 (zero).
• With increasing the magnetic field there is an increase in the value of magnetism and finally reaches point A which is called saturation point where B is constant.
• With a decrease in the value of the magnetic field, there is a decrease in the value of magnetism. But at B and H are equal to zero, substance or material retains some amount of magnetism is called retentivity or residual magnetism.
• When there is a decrease in the magnetic field towards the negative side, magnetism also decreases. At point C the substance is completely demagnetized.
• The force required to remove the retentivity of the material is known as Coercive force (C).
• In the opposite direction, the cycle is continued where the saturation point is D, retentivity point is E and coercive force is F.
• Due to the forward and opposite direction process, the cycle is complete and this cycle is called the hysteresis loop.

 

(b) Give the significance of following terms:

1. Current

Ans: Current is the rate at which electrons flow past a point in a complete electrical circuit.

2. Potential difference:

Ans : Potential difference is the work done in moving a unit of positive electric charge from one point to another.
The symbols for potential difference is V

3. Conductance

Ans: The reciprocal of resistance (G = 1/R).

The conductivity is a measure of the susceptibility of a material to the flow of electric current.

4. Electrical Power

Ans: Electric power is the rate at which work is done or energy is transferred in an electrical circuit.

5. Electrical Energy

Ans: Electrical energy is the energy derived from electric potential energy or kinetic energy of the charged particles

(c) Compare the characteristics of magnetic circuits and electric circuits.

 

Ans Electric Circuit and Magnetic Circuit

#	Content	Electrical Circuit	Magnetic Circuit
01	Basic Difference	In an electrical circuit, electric current flows through the closed path.	In the magnetic circuit, magnetic flux flows through the closed path.
02	Definition of electric current & magnetic flux	The number of free electrons or electric charge particles that move in the circuit is called ‘Electric Current (I)‘.	The number of magnetic lines of the force passing through a magnet is called ‘Magnetic Flux (ɸ)’.
03	Unit of current & flux	Electric current is measured in Ampere (A).	Magnetic flux is measured in Weber (Wb).
04	Circuit Role of electricity and magnetism	In an electrical circuit, electric current flows from positive to negative polarities.	In the magnetic circuit, magnetic flux flows from N-pole to S-pole.
05	Difference between electric force and magnetic force	In an electrical circuit, an electromotive force (EMF) is used to produce the electric current. Sometimes, EMF is known as electrical potential.	In the magnetic circuit, magnetomotive force (MMF) is used to produce the magnetic flux. Sometimes, MMF is known as magnetic potential.
06	Unit of EMF & MMF	EMF is measured in ‘Volt (V)’.	MMF is measured in ‘Ampere-turn (AT)’.
07	Opposition Property of circuits	In an electrical circuit, the resistance (R) opposes the flow of electric current.	In the magnetic circuit, the reluctance (S) opposes the flow of magnetic flux.
08	Unit of resistance & reluctance	The SI unit of resistance is ‘Ohm (Ω)’	The SI unit of reluctance is ‘Ampere- turn/Weber (AT/Wb)’
09	Flowing Property of circuits	Conductance (G) is the reciprocal of the resistance.	Permeance (P) is the reciprocal of reluctance.
10	Unit of conductance & permeance	Conductance is measured in ‘Siemens (S)’.	Permeance is measured in ‘Weber/Ampere-turn (Wb/AT)’ or ‘Henry (H)’
11	Ohm’s law	According to Ohm’s law of an electrical circuit is, Current (I) = (E/R) = (EMF/R)	According to Ohm’s law of the magnetic circuit is Flux (ɸ) = (F/S) = (MMF/S)
12	Kirchhoff’s Circuit Laws	For the electrical circuit, Kirchhoff current law (KCL) and Kirchhoff voltage law (KVL) are applicable.	For magnetic circuit, Kirchhoff MMF law and Flux law are applicable.
13	Kirchhoff’s first law	According to Kirchhoff’s first law of an electrical circuit is, Ʃ(I) = 0, at a node.	According to Kirchhoff’s first law of the magnetic circuit is, Ʃ(ɸ) = 0, at a node.
14	Kirchhoff’s second law	According to Kirchhoff’s second law of an electrical circuit is, Ʃ(IR) = Ʃ(EMF)	According to Kirchhoff’s second law, of the magnetic circuit is, Ʃ(ɸS) = Ʃ(MMF)
15	Current density & flux density	Current density (δ) is the rate of the electric currents flowing per unit cross-sectional area of a material.	Flux density (B) is the rate of the magnetic fluxes flowing per unit cross-sectional area of a material.
16	Unit of the current & flux density	The current density of an electrical circuit is measured in ‘Ampere/square*meter (A/m*m)’.	The flux density of a magnetic circuit is measured in ‘Weber/square*meter (Wb/m*m)’ or ‘Tesla (T)’.
17	Field intensity of electrical & magnetic circuits	Electric field strength is the electromotive force per unit electric charge. Sometimes, it is known as ‘electric field intensity (E)’.	Magnetic field strength is the magnetomotive force per unit length. It is known as ‘magnetic field intensity (H)’.
18	Unit of electric & magnetic field intensity	The SI unit of the electric field intensity is ‘Newton/Coulomb (N/C)’ or ‘Volt/Meter (V/m)’.	The SI unit of the magnetic field intensity is ‘Ampere/Meter (A/M)’
19	Circuit Structure	The electrical circuit can be a closed circuit or an open circuit.	The magnetic circuit is always a closed circuit.

                                                           Write any 7 point    

   OR

Q.2 (a) Explain the following

(i) Primary Cells

Ans: A primary cell or battery is the one that cannot easily be recharged after one use, and are discarded following discharge. These  cells are not chargeable because the electrode reaction occurs only once and after the use over a period of time the batteries become dead and cannot be reused.

(ii) Secondary Cells

Ans:  A secondary cell or battery is one that can be electrically recharged after its complete discharge. It is recharged by passing current through the circuit in the opposite direction to the current during discharge.

(iii) Dry Cells

Ans: A cell in which the electrolyte exists in the form of a paste, is absorbed in a porous medium, or is otherwise restrained from flowing.

(iv) Sealed rechargeable cells

Ans: Cells that are free from routine maintenance and can be operated without regard to position.

 

(b Mention the factors affecting resistance). Also, describe the effect of

temperature on resistance for pure metals, alloys, semi-conductors

and insulators.

Ans: Factor affecting resistance are:

·        Resistance is proportional to length. ...

·       Resistance is inversely proportional to cross-sectional-area. ...

·       Resistance depends on the material the wire is made of. ...

·       Resistance increases with the temperature of the wire.

 

With the increase in temperature, the random motion of electrons increases. As a result, the number of collisions of electrons with the positive ions increases in a metal. Hence, the resistance of a metal increases with increase in temperature.

 

The resistance of the semiconductor substances decreases with an increase in temperature. The resistivity of the semiconductor decrease exponentially with an increase in temperature

The materials which offer very high resistance and restrict the flow of electrons are called insulating materials. The insulating material has widespread use in electrical applications for preventing leakage current Thus, the resistance of the semiconductor and insulator decrease with an increase in temperature.

 

(c) Differentiate the characteristics of electrical and electronics systems. 05

Ans:

Basis For Comparison	Electrical Device	Electronics Device
Definition	It is defined as the device which uses the electrical energy for performing the work.	The device which controls the flow of electrons for performing the particular task is known as the electronics devices.
Material Used	Metals like copper and aluminum are used for the conduction of current.	Semiconductor material like silicon, germanium etc.
Operating Principle	Convert the electrical energy into other forms of energy.	Uses the electrical energy for performing the particular task.
Current	Alternating Current	Direct Current
Voltage	Works on high voltage.	Works on low voltage
Power consumption	More	Less
Manipulation	Do not manipulate the data	It manipulates the data.
Response Time	Fast	Slow
Required Space	More	Less
Safe	Less	More
Uses	For doing mechanical work.	For amplifying the weak signal or for coding and decoding the information.
Examples	Transformer, motor, generator etc.	Transistor, diode, microprocessor, flip-flop, amplifier, etc.

 

Q.3 (a) What is self and mutual inductance? Derive the expression for co-

efficient of self and mutual inductance.06

Ans: Self-inductance is the property of the current-carrying coil that resists or opposes the change of current flowing through it. This occurs mainly due to the self-induced emf produced in the coil itself.

Mutual inductance is the opposition to the change of current in one coil due to the presence of a second coil. 

Expression for self coefficient

We are considering a solenoid with nn turns with length ll . The area of cross section is A.

The solenoid carriers current I and B is the magnetic field inside the solenoid.
The magnetic field B is given as,

 

B=μ0nIl
Where, μ0 is the permeability of free space, n is the number of turns and I is the current in the solenoid and L is the length.

 

The magnetic flux is the product of the magnetic field and area of the cross section.
Here the magnetic flux per turn is given as,
ϕ=B×A
Substituting the values in the above expression,
ϕ=μ0nIl×A
Hence there is n number of turns, the total magnetic flux is given as,

ϕ=(μ0nI×A×n)./L

ϕ=μ0n2IA/L..............(1)

If L is the coefficient of self-inductance of the solenoid, then
ϕ=LI...........(2)
Comparing the two equations we get,

LI=μ0n2IA/L

                                                              L=μ0n2A/l

So the expression for the coefficient of self-inductance is 

μ0n2A/l

 

Mutual inductance

Let S1, and SS2 be two long solenoids of length l. the solenoid S2is wound closely over the solenoid S1as shown in the figure below.

.

Let N be the number of turns, B be the magnetic field and I be the current in the solenoids
Therefore, we know that magnetic field of solenoid S1

 is given by,

B1=μ0N1I1/l …………… (1)

The flux linked with solenoid 

S2S2

 is given by,

ϕ2=B1AN2

Therefore, from (1)
We get,

ϕ2=(μ0N1lI1)A×N2……………….. (2)
But we know that,

ϕ2=MI1……………… (3)
Where, M is he coefficient of mutual inductance
Therefore, from (2) and (3)
We get,

MI1=μ0N1N2AI1/l

Therefore,

M=μ0N1N2A/l

Therefore, the coefficient of mutual inductance between two given solenoids is 

M=μ0N1N2A/l

 

(b) Derive the expression for energy stored in a capacitor. 06

Ans: A capacitive circuit is shown in the above figure. In a circuit, with voltage around the capacitor V, the Capacitance C is given by the equation:
Q=CV…(1)

 

Where, Q represents the charge stored in the capacitor.
Now, we want to find the energy stored in a capacitor.
According to electrostatics, the energy stored in a capacitor will be equal to the work done to move the charge into the capacitor having an electrical potential V.
Or
dW=VdQ…(2)
Now, for a capacitor, V=QC …(3)
So, we can put the value of V from equation (3) into equation (2).
This gives,
dW=Q/CdQ,
Now the total work done to move charge Q can be found by integration,
∫W0dW=1/C
Now, from the integration method given in the formula used section, we can calculate the following result.

W=1/2Q2C

, This is also equal to the energy stored in the capacitor.
Therefore, U=0.5Q2/C
Moreover, from equation (1), we can put Q2=(CV)2
This will give us,
U=12Q2C

(c) What is cell? Classify different types of cells. Discuss the grouping of

cells for higher voltage and higher current requirements with

appropriate diagrams.

Ans: A primary cell or battery is one that cannot easily be recharged after one use, and are discarded following discharge. Most primary cells utilize electrolytes that are contained within absorbent material or a separator (i.e. no free or liquid electrolyte), and are thus termed dry cells.

A secondary cell or battery is one that can be electrically recharged after use to their original pre-discharge condition, by passing current through the circuit in the opposite direction to the current during discharge. The following graphic evidences the recharging process.

 

Secondary batteries fall into two sub-categories depending on their intended applications.

 

·       Cells that are utilized as energy storage devices, delivering energy on demand. Such cells are typically connected to primary power sources so as to be fully charged on demand. Examples of these type of secondary cells include emergency no-fail and standby power sources, aircraft systems and stationary energy storage systems for  Load levelling

 

·       Cells that are essentially utilized as primary cells, but are recharged after use rather than being discarded. Examples of these types of secondary cells primarily include portable consumer electronics and electric vehicles.

Combination of Two or More Cells

There are three types of combinations of cells:

• Series Combination: In a series combination, all the cells are connected side by side. The current through all the cells is the same. When two or more cells are connected in series, the combination is called ‘Battery’.

 

Series Combination

 

• Parallel Combination: In a parallel combination, all the cells are connected in a parallel manner. The voltage across all the cells may or may not be the same, depending upon the nature of all the cells.

 

Parallel Combination

 

• Mixed Combination: In a mixed combination, some cells are in series and other cells are in parallel.

 

 

Mixed Combination

 

Formula for Cells in Parallel

In a parallel combination, the cells are connected in parallel form. Consider ‘n’ cells of emf E₁, E₂, E₃,…, E_n and internal resistance r₁, r₂, r₃,…, r_n connected in parallel across a resistor of resistance ‘R’. The net current from all the cells will add up at the junction and form the equivalent current.

 

Ieq=I1+I2+I3+...+In

Req=E1r1+E2r2+E3r3+...+Enrn 

1Req=1r1+1r2+1r3+...+1rn

 

Formula for Cells in Series

In a series combination, the cells are connected in series form or side by side. Consider ‘n’ cells of emf E₁, E₂, E₃,…, E_n and internal resistance r₁, r₂, r₃,…, r_n connected in parallel across a resistor of resistance ‘R’. 

 

The value of current passing through all the cells will be the same. When two or more cells are connected in series, the emf of all the cells add up and we get a net emf. Also, since all the internal resistances are connected in series, the resistances will add up and we will get a net resistance.

Eeq=E1+E2+E3+...+En 

 Req=r1+r2+r3+...+rn 

 

Formula for Cells in Mixed Combination

In a mixed combination, the cells are connected both in series and parallel format. Consider ‘m’ rows in a parallel combination such that each row consists of ‘n’ cells of emf ‘E’ and internal resistance ‘r’. Consider that the whole combination is across an external resistance ‘R’. Here, ‘mn’ is a constant. 

In this case, the current is given by I=mnEmR+nr.

Also, the maximum current is drawn from the battery when external resistance matches the net internal resistance. The maximum current is given by max=mE2r.

 

3.a.What do you mean by statically and dynamically induced emf? Derive the expression for co-efficient of coupling. 06

Ans: Induced EMF

When a magnetic flux linking a conductor or coil changes, an electromotive force (EMF) is induced in the conductor or coil, is known as induced EMF. Depending upon the way of bringing the change in magnetic flux, the induced EMF is of two types −

·       Statically Induced EMF

·       Dynamically Induced EMF

Statically Induced EMF

When the conductor is stationary and the magnetic field is changing, the induced EMF in such a way is known as statically induced EMF (as in a transformer). It is so called because the EMF is induced in a conductor which is stationary. The statically induced EMF can also be classified into two categories −

·       Statically Induced EMF

·       Mutually Induced EMF

Self-Induced EMF

When an EMF is induced in the coil due to the change of its own magnetic flux linked with it is known as self-induced EMF.

Explanation − When a current flows in a coil, a magnetic field produced by this current through the coil. If the current in the coil changes, then the magnetic field linking the coil also changes. Therefore, according to Faraday’s law of electromagnetic induction, an EMF being induced in the coil. The induced EMF in such a way is known as self-induced EMF.

Mathematically, self-induced EMF is given by,

e=Ldidt...(1)

Where, L is the self-inductance of the coil.

Mutually Induced EMF

When an EMF is induced in a coil due to changing magnetic flux of neighbouring coil is known as mutually induced EMF.

Explanation − Consider two coils coil-1 and coil-2 placed adjacent to each other (see the figure). A fraction of the magnetic flux produced by coil-1 links with the coil-2. This magnetic flux which is common to both the coils 1 and 2 is known as mutual flux (φm)(φm). Now, if the current in coil-1 changes, the mutual flux also changes and thus EMF being induced in both the coils. The EMF induced in coil-2 is known as mutually induced EMF, since it is induced due changing in flux which is produced by coil-1. Mathematically, the mutually induced EMF is given by,

em=Mdi1dt...(2)

Where, M is the mutual inductance between the coils.

Dynamically Induced EMF

When the conductor is moved in a stationary magnetic field so that the magnetic flux linking with it changes in magnitude, as the conductor is subjected to a changing magnetic, therefore an EMF will be induced in it. The EMF induced in this way is known as dynamically induced EMF (as in a DC or AC generator). It is so called because EMF is induced in a conductor which is moving (dynamic).

Explanation − Consider a conductor of length l meters moving with a velocity of v m/s at right angles to a uniform stationary magnetic field of flux density B Wb/m².Let the conductor moves through a small distance dx in time dt seconds. Then,

Area swept by conductor,a=l×dxm^2

∴Magnetic flux  cut by conductor,dψ=Magnetic  FluxDensity×Area Swept

⟹dψ=BldxWb

Now, according to Faraday’s law of electromagnetic induction, the induced EMF will be,

e=Ndψ/dt=Bldx/dt(∵N=1)

∵dx/dt=Velocity(V)

∴e=BlvVolts...(3)

Equation (3) gives the dynamically induced EMF when the conductor moves at right angle to the magnetic field.

If the conductor moves at an angle &theta to the magnetic field, then the EMF induced due to only the perpendicular component of the velocity to the magnetic field.

e=Blvsinθ...(4))

(b) Describe the charging and discharging action of capacitor with appropriate voltage-charge characteristics. 06

Ans: Consider a capacitor connected in series with a resistor, to a constant DC supply through a switch S. 

‘C’ is the value of capacitance and ‘R’ is the resistance value. The ‘V’ is the Voltage of the DC source and ‘v‘ is the instantaneous voltage across the capacitor.

When the switch ‘S’ is closed, the current flows through the capacitor and it charges towards the voltage V from value 0. As the capacitor charges, the voltage across the capacitor increases and the current through the circuit gradually decrease. For an uncharged capacitor, the current through the circuit will be maximum at the instant of switching. And the charging currents reaches approximately equal to zero as the potential across the capacitor becomes equal to the Source voltage ‘V’.

Capacitor charging equation derivation steps,

Considering voltage law, the source voltage will be equal to the total voltage drop of the circuit.

Therefore,  

Rearrange the equation to perform the integration function,

RHS simplification,

On integrating we get,

As we are considering an uncharged capacitor (zero initial voltage), the value of constant ‘K ‘ can be obtained by substituting the initial conditions of the time and voltage. At the instant of closing the switch, the initial condition of time is t=0 and voltage across the capacitor is v=0.

Thus we get, logV=k  for t=0 and v=0.

Taking exponential on both sides,

From the above expression, it is clear that the instantaneous voltage will be a result of factors such as capacitance, resistance in series with the capacitor, time and the applied voltage value.

As the value of the constant RC increases, the value of exponential function also increases. That is the rate of voltage rise across the capacitor will be lesser with respect to time. That shows the charging time of the capacitor increase with the increase in the time constant RC. 

As the value of time ‘t’ increases, the term reduces and it means the voltage across the capacitor is nearly reaching its saturation value.

Charge q and charging current i of a capacitor

The expression for the voltage across a charging capacitor is derived as,

ν = V(1- e ^-t/RC)     → equation (1).

V – source voltage
ν – instantaneous voltage
C– capacitance
R – resistance
t– time

The voltage of a charged capacitor, V = Q/C.

Q– Maximum charge

The instantaneous voltage, v = q/C.

q– instantaneous charge

q/C =Q/C (1- e ^-t/RC)

q = Q (1- e ^-t/RC)

Charging current

For a capacitor, the flow of the charging current decreases gradually to zero in an exponential decay function with respect to time.

From the voltage law,

ν = V(1- e ^-t/RC)

ν = V – V e ^-t/RC

V – ν = V e ^-t/RC     →equation(2)

The source voltage, V =  voltage drop across the resistor (IR) + voltage across the capacitor ( ν ).

V = i R + ν

V – ν = i R

Substitute V – ν = i R in the equation 2.

Therefore, i R = V e ^-t/RC

 i = (V /R) e ^-t/RC

As V is the source voltage and R is the resistance,  V/R will be the maximum value of current that can flow through the circuit.

V/R =Imax

i = Imax e ^-t/RC

 

 

 

Capacitor Discharge Equation Derivation

For a discharging capacitor, the voltage across the capacitor v discharges towards 0.

Applying Kirchhoff’s voltage law, v is equal to the voltage drop across the resistor R.

The current i through the resistor is rewritten as above and substituted in equation 1.

By integrating and rearranging the above equation we get,

Applying exponential function,

The instantaneous voltage across a discharging capacitor is v = V e ^-t/RC

Instantaneous charge, q = Q e ^-t/RC

Instantaneous current, i = – Imax e ^-t/RC

From the above equations, it is clear that the voltage, current, and charge of a capacitor decay exponentially during the discharge. The discharge current has a negative sign because its direction is opposite to the charging current.

 

(c) Find the equivalent resistance for the following resistor combination circuit. 06

Ans: Find the equivalent resistance, R_EQ for the following resistor combination circuit.

Again, at first glance this resistor ladder network may seem a complicated task, but as before it is just a combination of series and parallel resistors connected together. Starting from the right hand side and using the simplified equation for two parallel resistors, we can find the equivalent resistance of the R₈ to R₁₀ combination and call it R_A.

R_A is in series with R₇ therefore the total resistance will be R_A + R₇ = 4 + 8 = 12Ω as shown.

This resistive value of 12Ω is now in parallel with R₆ and can be calculated as R_B.

R_B is in series with R₅ therefore the total resistance will be R_B + R₅ = 4 + 4 = 8Ω as shown.

This resistive value of 8Ω is now in parallel with R₄ and can be calculated as R_C as shown.

R_C is in series with R₃ therefore the total resistance will be R_C + R₃ = 8Ω as shown.

This resistive value of 8Ω is now in parallel with R₂ from which we can calculated R_D as:

R_D is in series with R₁ therefore the total resistance will be R_D + R₁ = 4 + 6 = 10Ω as shown.

                                                          Section 2

Q.4 (a) Select the most appropriate option. (Each of one mark) 06

 1. Reciprocal of Power Factor = _________? 

a. Demand Factor b. Diversity Factor c. Utilization Factor d. Q Factor                                         Ans:D

 

For reading purpose only.