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The CORRECT option is (c) R1=Ra+Rb+Ra*Rb/Rc, R2=Rc+Rb+Rc*Rb/Ra, R3=Ra+Rc+Ra*Rc/Rb

Explanation: After converting to delta, each delta CONNECTED RESISTANCE is EQUAL to the sum of the TWO resistance it is connected to+product of the two resistances divided by the remaining resistance. Hence R1=Ra+Rb+Ra*Rb/Rc, R2=Rc+Rb+Rc*Rb/Ra, R3=Ra+Rc+Ra*Rc/Rb.

The CORRECT answer is (a) 8/9ohm, 4/3ohm, 2/3ohm

The explanation is: Using the delta-star conversion FORMULA:

R1=4*3/(2+3+4)

R2=2*3/(2+3+4)

R3=2*4/(2+3+4).

Right CHOICE is (b) OPENED

The EXPLANATION: In SUPERPOSITION theorem when we consider the EFFECT of one voltage source, all the other current sources are opened and voltage sources are shorted.

Correct answer is (a) Shorted

To explain I WOULD say: In SUPERPOSITION theorem, WHETHER we consider the effect of a voltage or CURRENT source, voltage sources are always shorted and current sources are always OPENED.

The correct choice is (a) 30.77V, 7.52V, 18.82V

The BEST explanation: The nodal equations, considering V1, V2 and V3 as the first, second and third node respectively, are:

-8+(V1-V2)/3-3+(V1-V3)/4=0

3+V2+(V2-V3)/7+(v2-V1)/3=0

-2.5+(V3-V2)/7+(V3-V1)/4+V3/5=0

Solving the equations simultaneously, we GET V1=30.77V, V2=7.52V and V3=18.82V.

Right choice is (C) 1.29A, -0.566A, -1.91A

The explanation: Using the MATRIX method:

Matrix(3,-2,0) (I1)=(5)

(-2,9,-4) (I2)=(0)

(0,-4,9) (I3)=(-15)

Solving this matrix equation, we get I1 = 1.29A, I2 = -0.566A and I3 = -1.91A.

Right ANSWER is (a) 9.69 ohm, 35.71 ohm, 6.59 ohm

For EXPLANATION I would SAY: Using the star to DELTA conversion:

R1 = 4.53+6.66+4.53*6.66/1.23 = 35.71 ohm

R2 = 4.53+1.23+4.53*1.23/6.66 = 6.59 ohm

R3 = 1.23+6.66+1.23*6.66/4.53 = 9.69 ohm.

Correct option is (B) No

For explanation: We can use Norton’s theorem only for LINEAR NETWORKS. BJT is a non-linear network HENCE we cannot apply Norton’s theorem for it.

Correct choice is (b) 3.2V

To EXPLAIN I would say: When we consider the 16V source, we SHORT the 10V source and open the 15A and 3A source. From the resulting series circuit we can use voltage DIVIDER to find Vx.

Vx = 16*20/(20+80)=3.2A.

The correct CHOICE is (d) 29ohm

Easiest explanation: The equivalent resistance between NODE 1 and node 3 in the STAR connected circuit is R=(10×10+10×11+11×10)/11=29ohm.

The correct ANSWER is (b) 1.2ohm, 1.2ohm, 1.2ohm

The EXPLANATION: The 6 ohm and 9 ohm resistances are connected in parallel. Their equivalent resistances are: 6*9/(9+6)=3.6 ohm.

The 3 3.6 ohm resistors are connected in delta. Converting to STAR:

R1=R2=R3= 3.6*3.6/(3.6+3.6+3.6)=1.2 ohm.

The CORRECT option is (d) Resistances REMAIN the same

The BEST explanation: In source transformation, the value of the voltage and current sources change when changed from voltage to current source and current to voltage source but the value of the resistance REMAINS the same.

The correct answer is (b) In parallel with the CURRENT source

The best I can explain: When we perform source TRANSFORMATION on a circuit, we transform a voltage source connected in SERIES with a resistor to a current source connected in parallel to it. This is due to the relation we get by Ohm’s LAW, that is V=IR.

Correct choice is (b) No

Explanation: We can USE Thevenin’s theorem only for linear networks. BJT is a non-linear NETWORK hence we cannot APPLY Thevenin’s theorem for it.

Right option is (B) 3.67 ohm

The explanation is: Thevenin resistance is FOUND by opening the circuit between the SPECIFIED TERMINAL and shorting all VOLTAGE sources.

When the 10V source is shorted, we get:

Rth=(1||2)+3=3.67 ohm.

Correct option is (a) Rab*Rac/(Rab+Rbc+Rca)

For explanation I WOULD SAY: When converting from DELTA to star, the resistances in star connection is EQUAL to the product of the resistances it is connected to, divided by the total sum of the resistance.

Hence Rab*Rac/(Rab+Rbc+Rca).

The correct OPTION is (d) 50%

For EXPLANATION: Efficiency=(Power OUTPUT/ Power input)*100.

Power Output=I^2RL, Power Input=I^2(RL+RS)

Under MAXIMUM power transfer conditions, RL=RS

Power Output=I^2RL; Power Input=2*I^2RL

Thus efficiency=50%.

Correct choice is (b) Output

To EXPLAIN I would SAY: ACCORDING to Thevenin’s theorem, Vth is found across the output TERMINALS of a network and not the INPUT terminals.

Right answer is (b) 2V

The BEST I can EXPLAIN: Due to the effect of the 10V source, we short the 16V source and open the 3A and 15A source. From the RESULTING series circuit, we can use voltage DIVIDER to find the value of Vx.

Vx=10*20/(80+20)=2V.

Right answer is (a) 0.54A

The explanation: The 3 5 ohm RESISTORS are connected in delta. Changing it to STAR:

R1=R2=R3 = 1.67 ohm.

One of the 1.67 ohm resistors are connected in series with the 2 ohm resistor and another 1.67 ohm resistor is connected in series to the 3 ohm resistor.

The resulting network has a 1.67 ohm resistor connected in series with the parallel CONNECTION of the 3.67 and 4.67 resistors.

The equivalent RESISTANCE is 3.725A.

I=2/3.725 = 0.54A.

Correct choice is (a) Y-connection

To explain I would SAY: The star connection is also KNOWN as the Y-connection because its formation is LIKE the letter Y.

The correct answer is (a) Open circuit voltage

Explanation: Thevenin voltage is obtained by OPENING the SPECIFIED TERMINALS so it is open circuit voltage. It is not the short circuit voltage because if specified terminals are SHORTED voltage is equal to zero.

Right answer is (c) 8 OHM

Easy explanation: To FIND the value of I:

VI=P =>100I=1000 => I=10A.

Voltage ACROSS the 2 ohm resistor = 20V.

Voltage across the R resistor = 100-20= 80V.

R=V/I => R=80/10 = 8A.

Right choice is (c) 7.5V

The BEST I can explain: Taking the MESH currents in the THREE MESHES as I1, I2 and I3, the mesh equations are:

3I1+0I2+0V=5

-2I1-4I2+0V=0

0I1+9I2+V=0

Solving these equations simultaneously and taking the value of I2=0, we get V=7.5V.

Correct CHOICE is (a) LINEAR networks

To explain: Norton’s THEOREM works for only linear CIRCUIT ELEMENTS and not non-linear ones such as BJT, semiconductors etc.

Correct answer is (d) 4V

The BEST explanation: The NODAL equation is:

(V-10)/2+(V-7)/3+V/1=0

Solving for V, we GET V=4V.

Right choice is (d) 48V

The explanation: Due to the 3A source, we short the 16V and 10V source and open the 15A source. From the resulting circuit, we can use current divider to find the current in the 20 OHM branch and then multiply it with the resistance to find the voltage.

I20 = 3*80/(20+80)=2.4A

Vx=20*2.4=48V.

Correct choice is (a) KVL

The BEST explanation: KVL EMPLOYS mesh analysis to find the DIFFERENT mesh currents by finding the IR PRODUCTS in each mesh.

The correct choice is (c) RBC*RAC/(Rab+Rbc+Rca)

The explanation is: When converting from delta to star, the resistances in star connection is EQUAL to the product of the resistances it is connected to, divided by the total SUM of the resistance.

Hence Rac*Rbc/(Rab+Rbc+Rca).

Correct option is (c) RBC*Rab/(Rab+Rbc+Rca)

The EXPLANATION is: When converting from delta to star, the RESISTANCES in star connection is equal to the product of the resistances it is CONNECTED to, divided by the TOTAL sum of the resistance.

Hence Rab*Rbc/(Rab+Rbc+Rca).

Correct option is (c) Shorting all voltage SOURCES and opening all CURRENT sources

To ELABORATE: IDEAL current sources have infinite internal resistance hence behave like an open circuit whereas ideal voltage sources have ZERO internal resistance hence behave as a short circuit.

The correct option is (a) Voltage

The explanation is: NODAL analysis uses Kirchhoff’s CURRENT Law to find all the NODE voltages. Hence it is a method used to DETERMINE the voltage.

Right CHOICE is (b) CURRENT

The explanation: Mesh analysis uses Kirchhoff’s Voltage Law to FIND all the mesh currents. HENCE it is a method used to determine current.

The correct OPTION is (a) 1.54A, -0.189A, -1.195A

The explanation is: The three MESH equations are:

-3I1+2I2-5=0

2I1-9I2+4I3=0

4I2-9I3-10=0

Solving the equations, we get I1= 1.54A, I2=-0.189 and I3= -1.195A.

Correct ANSWER is (C) Power

The explanation is: Power ACROSS an element is not equal to the power across it due to all the other sources in the system. The power in an element is the product of the total voltage and the total current in that element.

Correct option is (c) Both PLANAR and non-planar networks

The BEST I can explain: Nodal ANALYSIS can be applied for both planar and non-planar networks SINCE each NODE, whether it is planar or non-planar, can be assigned a voltage.

Correct ANSWER is (b) 0.96A, -1.73A

To explain I would SAY: The TWO mesh EQUATIONS are:

5I1-3I2=10

-3I1+7I2=-15

Solving the equations SIMULTANEOUSLY, we get I1=0.96A and I2=-1.73A.

The CORRECT CHOICE is (b) Equal to

Easiest explanation: The circuit can draw maximum power only when source resistance is equal to the load resistance.