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# Multiple choice question for engineering

## Set 1

1. Find the equivalent delta circuit. a) 3ohm, 10ohm, 5ohm
b) 3ohm, 10ohm, 15ohm
c) 3ohm, 1ohm, 5ohm
d) 3ohm, 10ohm, 6ohm

Answer: a [Reason:] Using the star to delta conversion: R1=4.53+6.66+4.53*6.66/1.23 R2=4.53+1.23+4.53*1.23/6.66 R3=1.23+6.66+1.23*6.66/4.56.

2. Which, among the following is the correct expression for star-delta conversion?
a) R1=Ra*Rb/(Ra+Rb+Rc), R2=Rb*Rc/(Ra+Rb+Rc), R3=Rc*Ra/(Ra+Rb+Rc)b)
b) R1=Ra/(Ra+Rb+Rc), R2=Rb/(Ra+Rb+Rc), Rc=/(Ra+Rb+Rc)
c) R1=Ra+Rb+Ra*Rb/Rc, R2=Rc+Rb+Rc*Rb/Ra, R3=Ra+Rc+Ra*Rc/Rb
d) R1=Ra*Rb/Rc, R2=Rc*Rb/Ra, R3=Ra*Rc/Rb

Answer: c [Reason:] 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.

3. Find the equivalent resistance between X and Y. a) 3.33 ohm
b) 4.34 ohm
c) 5.65 ohm
d) 2.38 ohm

Answer: d [Reason:] The 3 2ohm resistors are connected in star, changing them to delta, we have R1=R2=R3= 2+2+2*2/2=6 ohm. The 3 6ohm resistors are connected in parallel to the 10 ohm 5 ohm and 10ohm resistors respectively. This network can be further reduced to a network consisting of a 3.75ohm and 2.73ohm resistor connected in series whose resultant is intern connected in parallel to the 3.75 ohm resistor.

4. Delta connection is also known as____________
a) Y-connection
b) Mesh connection
c) Either Y-connection or mesh connection
d) Neither Y-connection nor mesh connection

Answer: b [Reason:] Delta connection is also known as mean connection because its structure is like a mesh, that is, a closed loop.

5. Rab is the resistance between the terminals A and B, Rbc between B and C and Rca between C and A. These 3 resistors are connected in star connection. After transforming to delta, the resistance at A will be?
a) Rc+Rb+Rc*Rb/Ra
b) Rc+Rb+Ra*Rb/Rc
c) Ra+Rb+Ra*Rc/Rb
d) Rc+Rb+Rc*Ra/Rb

Answer: a [Reason:] After converting to delta, each delta connected resistance is equal to the sum of the two resistances it is connected to+product of the two resistances divided by the remaining resistance. Hence, resistance at A= Ra+Rb+Ra*Rb/Rc.

6. Rab is the resistance between the terminals A and B, Rbc between B and C and Rca between C and A. These 3 resistors are connected in star connection. After transforming to delta, the resistance at B will be?
a) Ra+Rb+Ra*Rb/Rc
b) Ra+Rc+Ra*Rc/Rb
c) Ra+Rb+Ra*Rc/Ra
d) Ra+Rc+Ra*Rb/Rc

Answer: b [Reason:] After converting to delta, each delta connected resistance is equal to the sum of the two resistances it is connected to+product of the two resistances divided by the remaining resistance. Hence, resistance at B= Ra+Rc+Ra*Rc/Rb.

7. Rab is the resistance between the terminals A and B, Rbc between B and C and Rca between C and A. These 3 resistors are connected in star connection. After transforming to delta, the resistance at C will be?
a) Rc+Rb+Ra*Rb/Rc
b) Ra+Rb+Ra*Rc/Rb
c) Ra+Rb+Ra*Rb/Rc
d) Ra+Rc+Ra*Rc/Rb

Answer: c [Reason:] 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, resistance at C= Ra+Rb+Ra*Rb/Rc.

8. If a 1ohm 2ohm and 32/3ohm resistor is connected in star, find the equivalent delta connection.
a) 1ohm, 3ohm, 2ohm
b) 4ohm, 3ohm, 5ohm
c) 4ohm, 5ohm, 2ohm
d) 5ohm, 3ohm, 2ohm

Answer: a [Reason:] Using the formula for delta to star conversion: R1=1+2+1*2/(32/3) R2=1+32/3+1*32/3/2 R3=2+32/3+2*32/3/1.

9. If a 8/9ohm, 4/3ohm and 2/3ohm resistor is connected in star, find its delta equivalent.
a) 4ohm, 3ohm, 2ohm
b) 1ohm, 3ohm, 2ohm
c) 4ohm, 1ohm, 2ohm
d) 4ohm, 3ohm, 1ohm

Answer: a [Reason:] Using the formula for star to delta conversion: R1=8/9+4/3+(8/9)*(4/3)/(2/3) R2=8/9+2/3+(8/9)*(2/3)/(4/3) R3=2/3+4/3+(2/3)*(4/3)/(8/9).

10. Find the equivalent resistance between A and B. a) 32ohm
b) 31ohm
c) 30ohm
d) 29ohm

Answer: d [Reason:] The equivalent resistance between node 1 and node 3 in the star connected circuit is R=(10×10+10×11+11×10)/11=29ohm.

## Set 2

1. In superposition theorem, when we consider the effect of one voltage source, all the other voltage sources are____________
a) Shorted
b) Opened
c) Removed
d) Undisturbed

Answer: a [Reason:] In superposition theorem when we consider the effect of one voltage source, all the other voltage sources are shorted and current sources are opened.

2. In superposition theorem, when we consider the effect of one current source, all the other voltage sources are____________
a) Shorted
b) Opened
c) Removed
d) Undisturbed

Answer: a [Reason:] 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.

3. In superposition theorem, when we consider the effect of one voltage source, all the other current sources are____________
a) Shorted
b) Opened
c) Removed
d) Undisturbed

Answer: b [Reason:] In superposition theorem when we consider the effect of one voltage source, all the other current sources are opened and voltage sources are shorted.

4. In superposition theorem, when we consider the effect of one current source, all the other current sources are____________
a) Shorted
b) Opened
c) Removed
d) Undisturbed

Answer: b [Reason:] In superposition theorem, whether we consider the effect of a voltage or current source, current sources are always opened and voltage sources are always shorted.

5. Find the value of Vx due to the 16V source. a) 4.2V
b) 3.2V
c) 2.3V
d) 6.3V

Answer: b [Reason:] 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.

6. Find Vx due to the 3A source. a) 56V
b) 78V
c) 38V
d) 48V

Answer: d [Reason:] 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.

7. Find the value of Vx due to the 10V source. a) 1V
b) 2V
c) 3V
d) 4V

Answer: b [Reason:] 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.

8. Find the voltage due to the 15A source.
a) 0V
b) 2V
c) 4V
d) 6V

Answer: a [Reason:] Due to the 15V source, the 10V and 16V sources get shorted and the 3A source acts as an open circuit. Since the 10V source is shorted, it acts as a low resistance path and current flows only within that loop and do not flow to the 20 ohm resistor. Hence the voltage is 0V.

9. Superposition theorem is valid for_________
a) Linear systems
b) Non-linear systems
c) Both linear and non-linear systems
d) Neither linear nor non-linear systems

Answer: a [Reason:] Superposition theorem is valid only for linear systems because the effect of a single source cannot be individually calculated in a non-linear system.

10. Superposition theorem does not work for________
a) Current
b) Voltage
c) Power
d) Works for all: current, voltage and power

Answer: c [Reason:] 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.

## Set 3

1. Which, among the following, is the formula for induced emf?
a) e=d(phi)/dt
b) e=dt/d(phi)
c) e=t*phi
d) e=t2phi

Answer: a [Reason:] The formula foe induced emf is e=d(phi)/dt because the induced emf is the flux linkage per unit time.

2. The formula for induced emf is _______
a) emf=B2l
b) emf=Bil
c) emf=Blv
d) emf=B2v

Answer: c [Reason:] The formula for induced emf is: emf=Blv, where B is the magnetic field, l is the length of the conductor and v is the velocity with which it is moving in the magnetic field.

3. If a conductor 0.2m long moves with a velocity of 0.3m/s in a magnetic field of 5T, calculate the emf induced.
a) 0.3V
b) 0.03V
c) 30V
d) 3V

Answer: a [Reason:] The formula for induced emf is: emf=Blv. Substituting the values of B, l and v from the question, we get emf=0.3V.

4. Find the length of a conductor which is moving with a velocity 0.4m/s in a magnetic field of 8T, inducing an emf of 20V.
a) 50m
b) 5m
c) 6.25m
d) 0.5m

Answer: c [Reason:] The formula for induced emf is: emf=Blv. Substituting the values of B, emf and v from the question, we get l=6.25m.

5. Find the strength of magnetic field in a conductor 0.5m long moving with a velocity of 10m/s, inducing an emf of 20V.
a) 1T
b) 2T
c) 3T
d) 4T

Answer: d [Reason:] The formula for induced emf is: emf=Blv. Substituting the values of l, emf and v from the question, we get B=4T.

6. What is emf?
a) Force
b) Voltage
c) Current
d) Flux

Answer: b [Reason:] Electromotive force is not actually a force. It is basically a voltage. It is the voltage developed by any source of electrical energy.

7. An E.M.F. can be induced by _________
a) Change in magnetic field
b) Change in the area of cross section
c) Change in angle between magnetic field and area
d) Change in magnetic field, area and angle

Answer: d [Reason:] The dot product of magnetic field vector and area vector. emf=BAcos(theta), hence if either of the three, that is, magnetic field, area or angle changes, thee emf will change.

8. The emf induced in a coil having N turns is?
a) e=phi/t
b) e=N*phi/t
c) e=N*phi*t
d) e=N2*phi*t

Answer: b [Reason:] The emf induced in a coil having N turns is, e=N*phi/t. This is because, the emf in a single coil is the flux linkage per unit time, that is, phi/t. Hence the flux induced in N turns is N*phi/t.

9. The total number of magnetic field lines passing through an area is termed as ________
a) Voltage
b) EMF
c) Magnetic flux
d) Magnetic flux density

Answer: b [Reason:] The number of magnetic flux lines per unit area is the magnetic flux, because flux is the number of field lines per unit area.

10. What is the consequence of motor effect?
a) Current
b) Voltage
c) Electromagnetic induction
d) EMF

Answer: c [Reason:] Motor effect is when a current carrying conductor in a magnetic field experiences a force, hence its consequence is electromagnetic induction.

## Set 4

1. Calculate the Thevenin resistance across the terminal AB for the following circuit. a) 4.34 ohm
b) 3.67 ohm
c) 3.43 ohm
d) 2.32 ohm

Answer: b [Reason:] 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.

2. Calculate Vth for the given circuit. a) 5.54V
b) 3.33V
c) 6.67V
d) 3.67V

Answer: c [Reason:] 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. Vth is calculated by opening the specified terminal. Using voltage divider, Vth= 2*10/(2+1)=6.67V.

3. Calculate the current across the 4 ohm resistor. a) 0.86A
b) 1.23A
c) 2.22A
d) 0.67A

Answer: a [Reason:] 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. Vth is calculated by opening the specified terminal. Using voltage divider, Vth= 2*10/(2+1)=6.67V. On drawing the Thevenin equivalent circuit, we get Rth, 4 ohm and Vth in series. Applying ohm’s law, I=Vth/(4+Rth)= 0.86A.

4. The Thevenin voltage is the__________
a) Open circuit voltage
b) Short circuit voltage
c) Both open circuit and short circuit voltage
d) Neither open circuit nor short circuit voltage

Answer: a [Reason:] Thevenin voltage is the open circuit voltage. It is the voltage across the specified terminals. It is not the short circuit voltage because short circuit voltage is equal to zero.

5. Thevenin resistance is found by ________
a) Shorting all voltage sources
b) Opening all current sources
c) Shorting all voltage sources and opening all current sources
d) Opening all voltage sources and shorting all current sources

Answer: c [Reason:] Current sources have infinite internal resistance hence behave like an open circuit whereas ideal voltage sources have 0 internal resistance hence behave as a short circuit.

6. Thevenin’s theorem is true for __________
a) Linear networks
b) Non-Linear networks
c) Both linear networks and nonlinear networks
d) Neither linear networks nor non-linear networks

Answer: a [Reason:] Thevenin’s theorem works for only linear circuit elements and not non-linear ones such as BJT, semiconductors etc.

7. In Thevenin’s theorem Vth is__________
a) Sum of two voltage sources
b) A single voltage source
c) Infinite voltage sources
d) 0

Answer: b [Reason:] Thevenin’s theorem states that a combination of voltage sources, current sources and resistors is equivalent to a single voltage source V and a single series resistor R.

8. Vth is found across the ____________ terminals of the network.
a) Input
b) Output
c) Neither input nor output
d) Either input or output

Answer: b [Reason:] According to Thevenin’s theorem, Vth is found across the output terminals of a network and not the input terminals.

9. Which of the following is also known as the dual of Thevenin’s theorem?
a) Norton’s theorem
b) Superposition theorem
c) Maximum power transfer theorem
d) Millman’s theorem

Answer: a [Reason:] Norton’s theorem is also known as the dual of Thevenin’s theorem because in Norton’s theorem we find short circuit current which is the dual of open circuit voltage-what we find in Thevenin’s theorem.

10. Can we use Thevinin’s theorem on a circuit containing a BJT?
a) Yes
b) No
c) Depends on the BJT
d) Insufficient data provided

Answer: b [Reason:] 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.

## Set 5

1. A CR network is one which consists of _________
a) A capacitor and resistor connected in parallel
b) A capacitor and resistor connected in series
c) A network consisting of a capacitor only
d) A network consisting of a resistor only

Answer: b [Reason:] A CR network is one which consists of a capacitor connected in series with a resistor. The capacitor discharges or charges through the resistor.

2. At DC, capacitor acts as _________
a) Open circuit
b) Short circuit
c) Resistor
d) Inductor

Answer: a [Reason:] At DC, the capacitor acts as open circuit because the capacitive resistance is infinity. The frequency of a DC circuit is 0. The capacitive resistance=1/(2*pi*f*C). Therefore, if the frequency is 0, the capacitive resistance is infinity and it acts as an open circuit.

3. In an RC series circuit, when the switch is closed and the circuit is complete, what is the response?
a) Response does not vary with time
b) Decays with time
c) Increases with time
d) First increases, then decreases

Answer: b [Reason:] In an RC series circuit, the response decays with time because according to the equation, there is an exponential decrease in the response.

4. If the switch is clocked at t=0, what is the current in the circuit? a) 0A
b) 10A
c) 20A
d) Infinity

Answer: b [Reason:] As soon as the switch is closed at t=0, the capacitor acts as a short circuit. The current in the circuit is: I=V/R= 100/10= 10A.

5. Calculate the voltage across the capacitor at t=0. a) 0A
b) 10A
c) 20A
d) Infinity

Answer: a [Reason:] When the switch is closed at t=0, the capacitor has no voltage across it since it has not been charged. The capacitor acts as a short circuit and the voltage across it is zero.

6. Calculate di(0)/dt if the switch is closed at t=0. a) -9.9A/s
b) -10A/s
c) 0A/s
d) -0.1A/s

Answer: a [Reason:] Applying KVL to the given circuit, we get: 100+10i(0)+1/10*integral(i(0)dt)=0 Differentiating once, we get: 10di(0)/dt+1/10*i. From the previous questions, we know that i(0)=10A. Substituting the values in the equation, we get di(0)/dt=-0.1A/s.

7. Calculate d2i(0)/dt2 from the given circuit. a) 10-6A/s2
b) 10-3A/s2
c) 106A/s2
d) 103A/s2

Answer: b [Reason:] Applying KVL to the given circuit, we get: 100+10i(0)+1/10*integral(i(0)dt)=0 Differentiating once, we get: 10di(0)/dt+1/10*i. Differentiating once again, we get: 10d2i(0)/dt2+10di(0)/dt=0. Substituting the values of di/dt from the previous explanation, we get d2i(0)/dt2=10-3A/s2.

8. The current equation for the given circuit is? a) i=10e(-0.01)t A
b) i=10e(0.01)t A
c) i=10e(-0.001)t A
d) i=100e(-0.01)t A

Answer: a [Reason:] The KVL equation is: 100+10i(0)+1/10*integral(i(0)dt)=0 On applying Laplace transform to this equation, we get: 100/s=I(s)/10s+10I(s) Solving the equation, we get: i=10e(-0.01)t A.

9. The expression for current in an RC circuit is?
a) i=(V/R)e(t/RC )
b) i=(V/R)e(-t/RC )
c) i=(V/R)/e(t/RC )
d) i=(V/R)/e(-t/RC ) 