Electrical Engineering Test

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Electrical Engineering Test - 3

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Question 1
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A parallel plate air capacitor as shown below has a total charge Q and a breakdown voltage V. A slab of a dielectric constant 6 is inserted as shown. The maximum breakdown voltage and the charge at this voltage respectively would be

A
V and 3.5 Q

B
3.5 V and Q

C
V/6 and 3Q

D
6V and 3Q

Solution

Concept:

The capacitance is given by the formula:

Analysis:

The two capacitors developed are in parallel. Hence the breakdown voltage of the combined capacitor will remain V.

Since the total charge stored Q will be C × V, we can write:

Q_eq = 3.5 Q
Question 2
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For a n-variable Boolean logic expression, the minimum and maximum possible number of essential prime implicants are ______ and ______ respectively.

A
n, 2ⁿ

B
0, 2^n-1

C
1, 2(n – 1)

D
0, 2ⁿ
Solution
In a n-variable Boolean function,
- The minimum number of prime implicants are 1
- The minimum number of essential prime implicants are 0
- The maximum number of prime implicants are 2^n-1
- The maximum number of essential prime implicants are 2^n-1
Example:

Consider the following 4-variable K-map,

In the above K-map representation, all the 1’s are part of more than one group. Therefore, there are no essential prime implicants.

Consider the following 4-variable K-map,

In the above K-map representation, the maximum number of essential prime applicants = maximum number of prime applicants = 2^n-1 = 2^{4 -1} = 8
Question 3
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A 2 pole, 50 Hz single phase induction motor running at 2600 rpm has an effective rotor resistance and reactance each of 0.5 Ω. The stator impedance and magnetizing current are to be neglected. The frequencies of rotor current in forward branch and in backward branch are to be respectively

A
16.67 Hz, 103.33 Hz

B
6.67 Hz, 93.33 Hz

C
93.33 Hz, 6.67 Hz

D
103.33 Hz, 16.67 Hz

Solution
Question 4
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Let V_sc is the voltage required to circulate rated current on short circuit, θ_sc is the power factor angle on short circuit, and θ₂ is the load power factor angle and E₂ is the secondary rated voltage. The Per unit voltage regulation of a transformer is given by

A

B

C

D

Solution

The transformer equivalent circuit under short-circuit is shown below.
Question 5
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A power system consists of 300 buses out of which 20 buses are connected with generators, 25 buses are the ones with controlled reactive power support and 15 buses are the ones with fixed shunt capacitors. All other buses are load buses. It is proposed to perform a load flow analysis using Newton-Rapson method. The size of the Newton-Rapson Jacobian matrix is

A
553 × 553

B
540 × 540

C
555 × 555

D
554 × 554

Solution

Given that:

Power system has 300 buses

n = total buses = 300

buses connected with generator = 20

buses with generator except slack bus (G) = 20 – 1 = 19

buses which controlled reactive power (Q) = 25

buses with fined shunt capacitor (C) = 15

Now, load buses = 300 – 20 – 25 – 15 = 240

Size of matrix = (2n – m - 2) × (2n – m - 2)

Where, m = total no. of P_v buses

m = Voltage controlled bus = Q + G

⇒ m = 25 + 19 = 44

(∵ fixed capacitor supply constant reactive power therefore it is considered as load buses)

Now size of matrix = (2n – m - 2) × (2n – m - 2)

= (2 × 300 – 44 - 2) × (2 × 300 – 44 - 2)

= 554 × 554
Question 6
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A network is described by the state model as

ẋ₁ = -2x₁ + x₂

ẋ₂ = x₁ – 3x₂ + u

y = 2x₁

The system is

A
undamped (oscillatory)

B
under damped

C
critically damped

D
overdamped

Solution
Question 7
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A slip-ring induction motor is expected to be started by adding extra resistance in the rotor circuit. The benefit that is derived by adding extra resistance in the rotor circuit in comparison to the rotor being shorted is

A
The starting torque would be higher.

B
The power factor at start will be lower.

C
The starting current is higher.

D
The losses at starting would be lower.

Solution
Question 8
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At 50% of full load the armature current drawn by a dc shunt motor is 40 A when connected to a 200 V supply. By decreasing the field flux its speed is raised by 20%. This also causes a 10% increase in load torque. The armature resistance including the brushes is 1 ohm. Neglecting armature reaction and saturation the percentage change in field current will be

A
28.9%

B
24.6%

C
27.4%

D
21.6%

Solution
Question 9
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A
6,1,1

B
6,2,3

C
1,2,3

D
1,6,3

Solution
Question 10
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A
1

B
-1

C
2

D
0

Solution