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# Multiple choice question for engineering

## Set 1

1. Reciprocal of reluctance is __________
a) Permeance
b) Susceptibility
c) Resistance
d) Conductance

Answer: a [Reason:] The reciprocal of reactance is permeance. It is the ability of a material to allow the passage of magnetic lines of flux.

2. Reactance is ________________ to the length of the material.
a) Directly proportional
b) Inversely proportional
c) Not related
d) Depends on the area of the material

Answer: a [Reason:] The formula for reluctance is: S= l/∫0 ∫rA. From the formula, we can see that reluctance is directly proportional to the length of the material.

3. Reactance is ________________ to the area of cross section the material.
a) Directly proportional
b) Inversely proportional
c) Not related
d) Depends on the length of the material

Answer: b [Reason:] The formula for reluctance is: S= l/∫0 ∫rA. From the formula, we can see that reluctance is inversely proportional to the area of cross section of the material.

4. When the length of the material increases, what happens to reluctance?
a) Increases
b) Decreases
c) Remains the same
d) Becomes zero

Answer: a [Reason:] Reluctance is directly proportional to the length of the material hence as length increases, reluctance also increases.

5. When the area of cross section of the material increases, what happens to reluctance?
a) Increases
b) Decreases
c) Remains the same
d) Becomes zero

Answer: b [Reason:] Reluctance is inversely proportional to the area of cross section of the material hence as area increases, reluctance decreases.

6. Unit of reluctance is?
a) AWb
b) A2/Wb
c) Wb/A
d) A/Wb

Answer: d [Reason:] Reluctance is the force per unit flux, hence its unit is A/Wb.

7. The electrical equivalent of reluctance is?
a) Resistance
b) Inductance
c) Capacitance
d) Conductance

Answer: a [Reason:] Resistance is the opposition to the flow of charge, similarly reluctance is the opposition to the flow of magnetic flux.

8. As the magnetic field strength increases, reluctance?
a) Increases
b) Decreases
c) Remains the same
d) Becomes zero

Answer: a [Reason:] Reluctance is directly proportional to the strength of magnetic field, hence as the strength of magnetic field increases, the reluctance increases.

9. As the magnetic flux density increases, the reluctance _____________
a) Increases
b) Decreases
c) Remains the same
d) Becomes zero

Answer: b [Reason:] Reluctance is inversely proportional to the magnetic flux density, hence as magnetic flux density increases, reluctance decreases.

10. Calculate the reluctance when the magnetomotive force is 10A turns and the flux is 5Wb.
a) 0.5A/Wb
b) 5A/Wb
c) 10A/Wb
d) 2A/Wb

Answer: d [Reason:] We know that: F=phi*S Substituting the given values from the question: S=2A/Wb.

## Set 2

1. For addition and subtraction of phasors, we use the _________ form.
a) Rectangular
b) Polar
c) Either rectangular or polar
d) Neither rectangular nor polar

Answer: a [Reason:] For addition and subtraction of phasors, we use the rectangular form because in the rectangular form we can only add the real part and the complex part separately to get the total value.

2. For multiplication and division of phasors, we use ____________ form.
a) Rectangular
b) Polar
c) Either rectangular or polar
d) Neither rectangular nor polar

Answer: a [Reason:] For multiplication and division of phasors, we use the polar form because in the rectangular form we just multiply or divide the values and add or subtract the angles.

3. If a voltage of 2+5j and another voltage of 3+ 6j flows through two different resistors, connected in series, in a circuit, find the total voltage in the circuit.
a) 2+5j V
b) 3+6j V
c) 5+11j V
d) 5+10j V

Answer: c [Reason:] The total voltage in the circuit is the sum of the two voltages where we add the real parts and imaginary parts separately. Therefore, Vtotal= 5+11j V.

4. Find the total current in the circuit if two currents of 4+5j flow in the circuit.
a) 4+5j A
b) 4A
c) 5A
d) 8+10j A

Answer: d [Reason:] The total current in the circuit is the sum of the two currents where we add the real parts and imaginary parts separately. Therefore, Itotal= 8+10j A.

5. What is the correct expression of ω?
a) ω=2*pi
b) ω=2*pi*f
c) ω=pi*f
d) ω=2f2

Answer: b [Reason:] The correct expression for ω is ω=2*pi*f where f is the frequency of the alternating voltage or current.

6. Find the value of ω if the frequency is 5Hz?

Answer: b [Reason:] The expression for ω is ω=2*pi*f. Substituting the value of f from the question, we get ω=31.4 rad/s.

7. When one sine wave passes through the zero following the other, it is _________
b) Lagging
c) Neither leading nor lagging
d) Either leading or lagging

Answer: b [Reason:] The sine wave is said to lag because it passes though zero following the other, hence it crosses zero after the first wave, therefore it is said to lag.

8. A phasor has frozen at 30 degrees, find the value of the phase angle.
a) 30 degrees
b) 60 degrees
c) 120 degrees
d) 180 degrees

Answer: a [Reason:] The value of the phase angle is the value at which the phasor stops or freezes. Here, it freezes at 30 degree, hence the phase angle is 30 degrees.

9. The time axis of an AC phasor represents?
a) Time
b) Phase angle
c) Voltage
d) Current

Answer: b [Reason:] The time axis while measuring an AC sinusoidal voltage or current represents the phase angle when converting it to a phasor.

10. The length of the phasor represents?
a) Magnitude of the quantity
b) Direction of the quantity
c) Neither magnitude nor direction
d) Either magnitude or direction

Answer: a [Reason:] The length of the phasor arrow represents the magnitude of the quantity, whereas the angle between the phasor and the reference represents the phase angle.

## Set 3

1. In an RC series circuit ________
a) Applied voltage lags capacitor voltage
b) Applied voltage leads capacitor voltage
c) Current and voltage are in phase
d) Applied voltage and capacitive voltage are in phase

Answer: b [Reason:] In an RC circuit, the applied voltage leads the current in the circuit, hence the applied voltage leads the capacitive voltage.

2. Which, among the following is the correct expression for φ?
a) φ=tan-1(Xc/R)
b) φ=tan-1 (R/Xc)
c) φ=tan-1 (Xc*R)
d) φ=cos-1 (Xc/R)

Answer: a [Reason:] Form the impedance triangle, we get tanφ= Xc/R. Hence φ=tan-1 (Xc/R).

3. For an RC circuit, the phase angle is always ________
a) Positive
b) Negative
c) 0
d) 90

Answer: a [Reason:] For a series resistance and capacitance circuit, the phase angle is always a positive value because the current will always leads the voltage.

4. What is φ in terms of voltage?
a) φ=cos-1V/VR
b) φ=cos-1V*VR
c) φ=cos-1VR/V
d) φ=tan-1V/VR

Answer: c [Reason:] Form the voltage triangle, we get cosφ= VR/V. Hence φ=cos-1VR/V.

5. An RC network is one which consists of?
a) Resistor and capacitor in parallel
b) Resistor and capacitor in series
c) Resistor and inductor in parallel
d) Resistor and inductor in series

Answer: b [Reason:] An R-C network is a network which consists of a resistor which is connected in series to a capacitor.

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

Answer: a [Reason:] At DC, the inductor acts as short 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.

7. 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.

8. 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)

Answer: b [Reason:] The particular solution of the current equation is zero. Hence, the expression for the current in an RC circuit is: i=(V/R)e(-t/RC).

9. An 8microF capacitor is connected in series with a 0.5 megaohm resistor. The DC voltage supply is 200V. Calculate the initial charging current.
a) 100 microA
b) 500 microA
c) 400 microA
d) 1000microA

Answer: c [Reason:] In a series RC circuit, the initial charging current is: I=V/R= 200/(0.5*106)= 400*10-6 A= 400 microA.

10. While discharging, what happens to the current in the capacitive circuit?
a) Decreases linearly
b) Increases linearly
c) Decreases exponentially
d) Increases exponentially

Answer: c [Reason:] The equation for the value of current in a discharging capacitive circuit is: I=I0*e-t/RC. From this equation, we can see that the current is exponentially decreasing since e is raised to a negative power.

## Set 4

1. A resistance of 7 ohm is connected in series with an inductance of 31.8mH. The circuit is connected to a 100V 50Hz sinusoidal supply. Calculate the current in the circuit.
a) 2.2A
b) 4.2A
c) 6.2A
d) 8.2A

Answer: d [Reason:] XL=2*pi*f*L= 10ohm. Therefore the total impedance =sqrt(R2+XL2)=12.2ohm. V=IZ, therefore 100/12.2= 8.2A.

2. A resistance of 7 ohm is connected in series with an inductance of 31.8mH. The circuit is connected to a 100V 50Hz sinusoidal supply. Calculate the phase difference.
a) -55.1
b) 55.1
c) 66.1
d) -66.1

Answer: a [Reason:] φ=tan-1(XL/R)=55.1 Since this is an inductive circuit, the current will lag, hence φ= -55.1.

3. A resistance of 7 ohm is connected in series with an inductance of 31.8mH. The circuit is connected to a 100V 50Hz sinusoidal supply. Calculate the voltage across the resistor.
a) 31.8V
b) 57.4V
c) 67.3V
d) 78.2V

Answer: b [Reason:] XL=2*pi*f*L= 10ohm. Therefore the total impedance =sqrt(R2+XL2)=12.2ohm. V=IZ, therefore 100/12.2= 8.2A. Voltage across resistor= 8.2*7=57.4V.

4. A resistance of 7 ohm is connected in series with an inductance of 31.8mH. The circuit is connected to a 100V 50Hz sinusoidal supply. Calculate the voltage across the inductor.
a) 57.4V
b) 42.6V
c) 65.2V
d) 76.2V

Answer: b [Reason:] XL=2*pi*f*L= 10ohm. Therefore the total impedance =sqrt(R2+XL2)=12.2ohm. V=IZ, therefore 100/12.2= 8.2A. Voltage across resistor= 8.2*7=57.4V. Voltage across inductor =100-VR= 42.6V.

5. A resistance of 7 ohm is connected in series with an inductance of 31.8mH. The circuit is connected to a x V 50Hz sinusoidal supply. The current in the circuit is 8.2A. Calculate the value of x.
a) 10V
b) 50V
c) 100V
d) 120V

Answer: c [Reason:] XL=2*pi*f*L= 10ohm. Therefore the total impedance =sqrt(R2+XL2)=12.2ohm. V=IZ, Therefore V=12.2*8.2=100V.

6. Which, among the following, is the correct expression for φ.
a) φ=tan-1 (XL/R)
b) φ=tan-1 (R/XL)
c) φ=tan-1 (XL*R)
d) φ=cos-1 (XL/R)

Answer: a [Reason:] Form the impedance triangle, we get tanφ= XL/R. Hence φ=tan-1 (XL/R).

7. For an RL circuit, the phase angle is always ________
a) Positive
b) Negative
c) 0
d) 90

Answer: b [Reason:] For a series resistance and inductance circuit the phase angle is always a negative value because the current will always lag the voltage.

8. What is φ in terms of voltage?
a) φ=cos-1V/VR
b) φ=cos-1V*VR
c) φ=cos-1VR/V
d) φ=tan-1V/VR

Answer: c [Reason:] Form the voltage triangle, we get cosφ= VR/V. Hence φ=cos-1VR/V.

9. An RL network is one which consists of?
a) Resistor and capacitor in parallel
b) Resistor and capacitor in series
c) Resistor and inductor in parallel
d) Resistor and inductor in series

Answer: d [Reason:] An R-L network is a network which consists of a resistor which is connected in series to an inductor.

10. At DC, inductor acts as ___________
a) Open circuit
b) Short circuit
c) Resistor
d) Inductor

Answer: b [Reason:] At DC, the inductor acts as short circuit because the inductive resistance is zero. The frequency of a DC circuit is 0. The inductive resistance=(2*pi*f*L). Therefore, if the frequency is 0, the inductive resistance is zero and it acts as an short circuit.

## Set 5

1. Materials which allow the passage of electric current are known as______
a) Insulators
b) Conductors
c) Dielectrics
d) Semi-conductors

Answer: b [Reason:] Conductors are materials(mostly metals), which freely allow the passage of electrons through it. If electrons can flow freely through a material, it implies that even current can flow freely through that material since current is the rate of flow of electrons.

2. A wire of length 2m and another wire of length 5m are made up of the same material and have the same area of cross section, which wire has higher resistance?
a) Both have equal resistance
b) The 2m wire has higher resistance
c) The 5m wire has higher resistance
d) The value of resistance cannot be determined from the given data

Answer: c [Reason:] Resistance is directly proportional to the length of the wire, hence as the length of the wire increases, resistance increases.

3. A wire having an area of cross section = 10sqm and another wire having an area of cross section= 15sqm, have the same length and are made up of the same material. Which wire has more resistance?
a) Both have equal resistance
b) The 10sqm wire has higher resistance
c) The 15sqm wire has higher resistance
d) The value of resistance cannot be determined from the given data

Answer: b [Reason:] Resistance is inversely proportional to area of cross section. As area of cross section increases, resistance decreases. Hence the 10sqm wire has higher resistance than the 15sqm wire.

4. Which of the following statements are true with regard to resistance?
a) Resistance is directly proportional to length of the wire
b) Resistance is directly proportional to area of cross section of the wire
c) Resistance is inversely proportional to the length of the wire
d) All the statements are false

Answer: b [Reason:] The expression for resistance is: Resistance=Resistivity*length of wire/ area of cross section of wire. Hence resistance is directly proportional to length.

5. A wire has the same resistance as the one given in the figure. Calculate its resistivity if the length of the wire is 10m and its area of cross section is 2m. a) 16 ohm-metre
b) 8 ohm-metre
c) 16 kiloohm-metre
d) 8 kiloohm-metre

Answer: b [Reason:] From the given circuit, R=V/I= 200/5 =40ohm. Resistivity= Resistance*Area of cross section/ Length of the wire. Resistivity= 40*2/10= 8 ohm-metre.

6. Which, among the following is a unit for resistivity?
a) ohm/metre
b) ohm/metre2
c) ohm-metre
d) ohm-metre2

Answer: c [Reason:] Resistivity= RA/l= ohm*metre2/metre. Hence the unit of resistivity is ohm- metre.

7. What is the resistivity of Copper?
a) 1.59*10-8ohm-m
b) 2.7*10-8ohm-m
c) 7.3*10-8ohm-m
d) 5.35*10-8ohm-m

Answer: a [Reason:] Resistivity is a material property. Different materials have different resistivity’s. Resistivity depends on the material of the wire, hence the resistivity of copper is 1.59*10-8 ohm-metre.

8. Calculate the ratio of the resistivity of 2 wires having the same length and same resistance with area of cross section 2m2 and 5m2 respectively.
a) 5:7
b) 2:7
c) 2:5
d) 7:5

Answer: c [Reason:] Resistivity of first wire= RA1/l= 2R/l. Resistivity of second wire= RA2/l = 5R/l. Ratio of the first resistance to the second= (2A/l)/(5A/l)= 2/5.

9. Which of the following statements are true with regard to resistivity?
a) Resistance depends on the temperature
b) Resistance does not depend on the temperature
c) Resistance does not depend on length
d) All the statements are false