ISRO HSFC Technician B Electrician Solved Question paper

Answer: "1 "

The standard form of the equation of a circle is:

(x-h)² + (y-k)² = r²

where (h,k) is the center of the circle and r is the radius

Let’s complete the square for both x and y terms:

x² + 4x + y² + 2y + 4 = 0
(x² + 4x + 4) + (y² + 2y + 1- 1) = 0
(x + 2)² + (y + 1)² = 1

Now we can see that the equation is in the standard form with h = -2, k = -1, and r² = 1.

Therefore, the radius of the circle is the square root of r² which is 1.

Answer: "480 "

We are given that their sum is 24. So, we can write the equation:

x + (x+2) + (x+4) = 24

Simplifying this, we get:

3x + 6 = 24

Solving for x:

3x = 18

x = 6

Therefore, the three numbers are:

First number: x = 6

Second number: x+2 = 6+2 = 8

Third number: x+4 = 6+4 = 10

Now, let’s find their product:

6 * 8 * 10 = 480

So, the product of the three consecutive even integers is 480.

Answer: "6.3 "

To find the mean of the given data, we need to calculate the weighted average. Here, the frequencies (f) represent the weights of the corresponding values (x).

Steps to calculate the weighted mean:

1.  Multiply each value (x) by its corresponding frequency (f):

• 4 * 4 = 16
• 5 * 3 = 15
• 6 * 3 = 18
• 7 * 5 = 35
• 8 * 3 = 24
• 9 * 2 = 18

2. Add up all the products: 16 + 15 + 18 + 35 + 24 + 18 = 126

3. Add up all the frequencies: 4 + 3 + 3 + 5 + 3 + 2 = 20

4. Divide the sum of the products by the sum of the frequencies:

Mean = 126 / 20 = 6.3

Therefore, the mean of the given data is 6.3.

Answer: "Impedance "

The Q-meter is primarily used to measure the quality factor (Q-factor) of resonant circuits, which includes inductors and capacitors. It is also used to measure impedance, particularly in RF (radio frequency) applications.

Purpose:

• The Q-meter is primarily used for measuring impedance.

Principle of Operation:

• The Q-meter works on the principle of resonance. This means it operates at a specific frequency where the inductive and capacitive reactance in the circuit cancel each other out, resulting in maximum current flow.

3. Q-Factor:

• The Q-factor is a measure of the quality of a resonant circuit. It is defined as the ratio of the voltage across the capacitor (Vc) to the total applied voltage (V):

Q-Factor = Vc / V

• A higher Q value signifies a more efficient system with lower energy loss.

Answer: "Ductility "

Soldering is used to improve the bonding strength of wire joints.

When we connect wires, soldering creates a strong bond between them. This bond ensures a secure connection that can withstand physical stress and electrical current.

Benefits of soldering:

• Strong bond: Soldering creates a robust and durable connection.
• Electrical conductivity: Solder is a good conductor of electricity, ensuring efficient signal transmission.
• Corrosion resistance: Solder forms a protective layer that prevents corrosion.
• Heat resistance: Solder can withstand high temperatures.

While soldering improves conductivity and heat resistance, its primary purpose is to enhance the bonding strength of wire joints.

Answer: "7 "

Let’s assume the base of the number system is ‘x‘.

In base ‘x’, the numbers 25, 15, and 43 can be represented as:

• 25 in base x = 2x + 5
• 15 in base x = x + 5
• 43 in base x = 4x + 3

Now, we can set up the equation:

(2x + 5) + (x + 5) = 4x + 3

Solving this equation:

3x + 10 = 4x + 3

Subtracting 3x from both sides and subtracting 3 from both sides:

7 = x

Answer: "18 Wh "

Voltage across the Resistor:

• The charging voltage is 15V.
• The battery voltage increases linearly from 10V to 12V over 6 hours.
• To maintain a constant current of 1A, the voltage drop across the resistor must be constant.

Therefore, the voltage across the resistor is 15V – 12V = 3V.

2. Resistance of the Resistor:

Using Ohm’s law, we can calculate the resistance:

R = V / I

= 3V / 1A = 3Ω

3. Energy Dissipated in the Resistor:

The energy dissipated in a resistor is given by the formula:

Energy = Power × Time = (I²)R × t

where:

• I = Current = 1A
• R = Resistance = 3Ω
• t = Time = 6 hours

So, the energy wasted is:

Energy = (1²) × 3 × 6 =  18 Wh

Answer: "2.5 Hz "

We have a 6-pole, 3-phase induction motor operating at 950 RPM when connected to a 50 Hz supply. We need to find the frequency of the rotor current.

Synchronous Speed (Ns):

• Ns = (120 * f) / P

Where

Ns = Synchronous speed in RPM
f = Supply frequency in Hz
P = Number of poles

Ns = (120 * 50) / 6 = 1000 RPM

Slip (s):

• Slip (s) = (Ns – Nr) / Ns
• Where Nr = Rotor speed in RPM
• s = (1000 – 950) / 1000 = 0.05

Rotor Current Frequency (fr):

• fr = s * f
• fr = 0.05 * 50 = 2.5 Hz

Answer: "20 W "

We have an ideal transformer with:

• Primary turns (N₁) = 1000
• Secondary turns (N₂) = 50
• Primary voltage (V₁) = 200 V (RMS)
• Load resistance (R₂) = 5 ohms

We need to calculate the input power.

Calculate Secondary Voltage (V₂):

In an ideal transformer

V₁/V₂ = N₁/N₂ V₂

= (N₂/N₁) * V₁ V₂ = (50/1000) * 200 = 10 V

Calculate Secondary Current (I₂):

Using Ohm’s law,

I₂ = V₂/R₂

I₂ = 10 V / 5 Ω = 2 A

Calculate Input Power (P₁):

In an ideal transformer, input power equals output power.

P₁ = P₂ = V₂ * I₂

P₁ = 10 V * 2 A = 20 W

Answer: "Suppress dV/dt "

Snubber Circuit: A Protective Shield for Power Devices

• A snubber circuit is a protective circuit element commonly used in power electronic systems. Its primary function is to suppress the high-voltage transients (spikes) that can occur during the switching process of power devices like transistors, diodes, and thyristors.

Why is Suppressing dV/dt Important?

When a power device switches rapidly, it can induce high-voltage spikes due to parasitic inductances and capacitances in the circuit. These spikes can lead to:

• Device Damage: Excessive voltage stress can damage the device.
• Electromagnetic Interference (EMI): These spikes can generate electromagnetic interference, affecting other electronic devices.
• Switching Losses: High-voltage spikes can increase switching losses, reducing the efficiency of the power converter.

How a Snubber Circuit Works:

A typical snubber circuit consists of a resistor (R) and a capacitor (C) connected in parallel across the power device. When the device switches, the capacitor absorbs the excess energy, limiting the rate of voltage rise (dV/dt). The resistor dissipates the energy stored in the capacitor.

Slow down the rate of voltage change (dV/dt): By providing an alternative path for the current, the snubber limits the voltage across the switching device, reducing dV/dt.