SSC JE Electrical Previous Year Question Paper 2018-SET 4|MES Electrical

Inductance is defined as the ratio of Magnetic Flux to the current.

Inductance = Magnetic Flux / Current——-(1)

Magnetic Flux  = Magnetic field × Area

Magnetic field = Force ⁄ current × Length…………(since F = BIL)

Force = Mass × Acceleration

Acceleration = Velocity ⁄ Time

Velocity = Displacement / Time

Now we will start solving all the from the bottom i.e from the velocity

Displacement, Length = L & Time = T , Mass = M , Current = A

⇒ Velocity = Displacement / Time

Velocity = [ M L T⁻¹]

⇒ Acceleration = Velocity ⁄ Time = [ M⁰ L T⁻¹] ⁄ [T]

Acceleration = [M⁰ L T⁻²] 

⇒ Force = Mass × Acceleration = [M] × [M⁰ L T⁻²] 

Force = [M L T⁻²] 

⇒ Magnetic field = Force ⁄ current × Length = [M L T⁻²]  ⁄ [A × L]

Magnetic field = [M L⁰ T⁻² A⁻¹]

⇒  Magnetic Flux  = Magnetic field × Area = [M L⁰ T⁻² A⁻¹] × [L²] ……..(since Area = L × B = L²)

Magnetic Flux  = [M L² T⁻² A⁻¹]

⇒  Inductance = Magnetic Flux / Current = [M L² T⁻² A⁻¹] ⁄ [A]

Inductance = [M L² T⁻² A⁻²]

Note:-  Charge Q = Current × Time = [AT]

∴ Inductance = [M L² Q⁻²] or [M L² ⁄ Q²]

Recording instruments: These instruments give a continuous record of the given electrical quantity which is being measured over a specific period.

In such recording Instruments, the readings are recorded by drawing the graph. The pointer of such instruments is provided with a marker i.e. pen or pencil, which moves on graph paper as per the reading. The X-Y plotter is the best example of such an instrument.

X-Y recorders are used for many measurements and tests as follows:-

• Speed/torque measurements of electric motors.
• Lift/drag wind-tunnel tests.
• Plotting of characteristic curves of vacuum tubes, transistors, rectifiers, zoner diodes, etc.
• Measurement of physical quantities, such as force, pressure, temperature, etc.
• Regulation curves of the power supply.
• Electrical characteristics of materials such as resistance vs. temperature
• Characteristics of governors, such as speed vs. load.

Note:- Ammeter, Voltmeter, Meggar all are Indicating Instrument

The reading of two wattmeters can be expressed as

W₁ =  V_LI_Lcos(30 + φ)
W₂ =  V_LI_Lcos(30 − φ)

(i) When PF is unity ( φ = 0°)

W₁ =  V_LI_Lcos30°
W₂ =  V_LI_Lcos30°

Both wattmeters read equal and positive reading i.e upscale reading

(ii) When PF is 0.5 (φ = 60°)

W₁ =  V_LI_Lcos90° = 0
W₂ =  V_LI_Lcos30°

Hence total power is measured by wattmeter W₂ alone

(iii) Power Factor Is More Than 0.5 But Less Than One (i.e.,1 > cosφ > 0.5) or 60° > φ > 0°

Under such conditions, the readings of the wattmeter will be

W₁ =  V_LI_Lcos(30 + φ) (positive, larger)
W₂ =  V_LI_Lcos(30 − φ) (negative, smaller)

Hence when the power factor is more than 0.5 but less than one, both me wattmeters give positive (upscale) readings. However, wattmeter W₁ gives larger reading than wattmeter W₂.

Now, total power, P = W₁ + W₂ = larger reading + smaller readings

(iv) When PF is less than 0.5 but greater than 0 i.e ( 90° > φ > 60°)

W₁ = Negative
W₂ = positive (since cos(−φ) = cosφ)

The wattmeter W₂ reads positive (i.e.upscale) because for the given conditions (i.e. ( 90° > φ > 60°), the phase angle between voltage and current will be less than 90°. However, in wattmeter W₁, the phase angle between voltage and current shall be more than 90° and hence the wattmeter gives a negative (i.e. downscale) reading.

Wattmeter cannot show a negative reading as it has only a positive scale. An indication of negative reading is that the pointer tries to deflect in a negative direction i.e. to the left of zero. In such case, reading can be converted to positive by interchanging either pressure coil connections or by interchanging current coil connections. Remember that interchanging connections of both the coils will have no effect on wattmeter reading.

 (v) When P.F reads zero (φ = 90°)

Such a case occurs when the load consist of pure inductance or pure capacitance

W₁ =  V_LI_Lcos(30 + 90°) = – V_LI_Lsin30°
W₂ =  V_LI_Lcos(30 − 90°) = V_LI_Lsin30°

In this condition, the two wattmeter reads equal and opposite i.e W₁ + W₂ = 0

Extension of Ammeter Range

The current range of a DC moving coil ammeter is extended by connecting a shunt resistance Rs (low resistance) across the coil, the circuit as shown in Figure

I = Total current = 5A
I_m = full-scale deflection current of ammeter = ?
I_sh = shunt current
R_m = resistance of the ammeter = 25Ω
R_sh = shunt resistance = 75Ω

The full-scale deflection current I_m is given as

$\begin{array}{l}{I_m} = \dfrac{{I \times {R_{sh}}}}{{{R_m} + {R_{sh}}}}\\\\{I_m} = \dfrac{{5 \times 75}}{{(25 + 75)}}\\\\{I_m} = 3.75A\end{array}$

A multimeter is an indicating electronic instrument that can be used for the measurement of three quantities, namely voltage, current, and resistance. This instrument can also be used for both dc and ac voltages and currents. Multimeters are available in both analog and digital forms. Although analog multimeters are being replaced by digital multimeters.

The actual conversion of electrical to light energy takes place on the display screen when electrons strike a material known as a phosphor. A phosphor is a chemical that glows when exposed to electrical energy.

The selection of phosphors to be used in a cathode ray tube is very important. Many different phosphors are known, and each has special characteristics. For example, the phosphor known as yttrium oxide gives off a red glow when struck by electrons, and yttrium silicate gives off a purplish-blue glow.

Zinc sulfide with silver metal as an impurity gives off a bluish glow and with copper metal as an impurity, a greenish glow.

Instrument transformers are used in conjunction with an ammeter and voltmeter to extend the range of meters. In dc circuit shunt and multipliers are used to extend the range of measuring instruments. The shunt is used to extend the range of the ammeter whereas the multiplier is used to extend the range of voltmeters

This type of ammeter is shown in Figure. The primary of the transformer is connected in series with the load, and the ammeter is connected to the secondary of the transformer. Notice that the range of the meter is changed by selecting different taps on the secondary of the current transformer. The different taps on the transformer provide different turns-ratios between the primary and secondary of the transformer. The work is explained in detail.

• The current transformer is used to step down the current to a lower value so that the current can be measured with a normal range ammeter.
• The current transformer has a primary coil of one or more turns of thick wire having high cross-sectional area and it is connected in series.
• The primary of the current transformer is connected to the load or feeder while the secondary of the current transformer is connected to an ammeter.
• The impedance of the primary is very low, and the currents very high. The primary current is dependent on the load on the line rather than the load on the secondary circuit.
• Current drawn by the secondary has little effect on line current.
• The secondary of the transformer contains many turns of fine wire having a smaller cross-section area and has a much higher impedance. If the secondary is not loaded, this transformer acts to step up the voltage to a dangerous level, due to the high turns ratio. Because of this, a current transformer should always have a short-circuit placed across its secondary winding when connecting or removing any device from its output. By heavily loading the secondary, the high voltage is reduced to the safe level.
• The nominal current rating of the secondary winding of the CT is 5A to 1 A.
• To illustrate the operation of a current transformer, assume that the current ratio of the primary winding is 100 A. The secondary winding has a standard rating of 5A.
• The primary winding consists of three turns of wire, and the secondary winding consists of 60 turns.
• The ratio between the primary and the secondary currents is 100 A/5 A, or 20:1
• In other words, the primary current is 20 times greater than the secondary current.
• Note that the number of turns and the current in the primary and secondary windings are related by an inverse proportion. i.e I₁ / I₂ = N₂ / N_1.
• By increasing the number of secondary windings, N₂, the secondary current can be made much smaller than the current in the primary circuit being measured. In other words, as N2 increases, I₂ goes down by a proportional amount.

Induction-type Single-phase Energy Meter

An induction-type instrument can be used as an ammeter, voltmeter, or wattmeter, the induction-type energy meters are more popular. Induction-type single-phase energy meter is used invariably to measure the energy consumed in an AC circuit in a prescribed period where supply voltage and frequency are constant. The energy meter is an integrating instrument that measures the total quantity of electrical energy supplied to the circuit in a given period.

Principle

The basic principle of an induction-type energy meter is electromagnetic induction. When AC flows through two suitably located coils (current coil and potential coil), they produce the rotating magnetic field that is cut by the metallic disc suspended between the coils, and thus, an emf is induced in the disc that circulates eddy currents in it. By the interaction of rotating magnetic field and eddy currents, electromagnetic torque is developed that causes the disc to rotate. This is the same principle that is applied in single-phase induction motors.

A single-phase energy meter has four essential parts:

1. Operating system
2. Moving system
3. Braking system
4. Registering system

Operating System

The operating system consists of two electromagnets. The cores of these electromagnets are made of silicon steel laminations. The coils of one of these electromagnets (series magnet) are connected in series with the load and are called the current coil. The other electromagnet (shunt magnet) is wound with a coil that is connected across the supply, called the pressure coil. The pressure coil, thus, carries a current that is proportional to supply voltage.

Shading bands made of copper are provided on the central limb of the shunt magnet. Shading bands, as will be described later, are used to bring the flux produced by a shunt magnet exactly in quadrature with the applied voltage.

Moving System

The moving system consists of a light aluminum disc mounted on a spindle. The disc is placed in the space between the series and shunt magnets. The disc is so positioned that it intersects the flux produced by both the magnets. The deflecting torque on the disc is produced by an interaction between these fluxes and the eddy current they induce in the disc. In energy meters, there is no control spring as such, so there is the continuous rotation of the disc.

Braking System

The braking system in an induction type energy meter consists of a braking device which is usually a permanent magnet positioned near the edge of the aluminum disc. The arrangement is shown in Figure.

The emf induced in the aluminum disc due to relative motion between the rotating disc and the fixed permanent magnet (brake magnet) induces an eddy current in the disc. 

When the disc rotates in the air gap, eddy currents are induced in the disc which opposes the cause producing them i.e. relative motion of the disc with respect to the magnet. This eddy current, while interacting with the brake magnet flux, produces a retarding or braking torque.

This braking torque is proportional to the speed of the rotating disc. When the braking torque becomes equal to the operating torque, the disc rotates at a steady speed.

The position of the permanent magnet with respect to the rotating disc is adjustable. Therefore, braking torque can be adjusted by shifting the permanent magnet to different radial positions with respect to the disc.

Registering System

The function of a registering or counting system is to continuously record a numerical value that is proportional to the number of revolutions made by the rotating system.

Wien’s Bridge

Wien’s bridge is primarily used for the determination of an unknown frequency. However, it can be used for various other applications including capacitance measurement, in harmonic distortion analyzers, where it is used as the notch filter. and also in audio and HF oscillators.

Wien’s bridge is frequency sensitive. Thus, unless the supply voltage is purely sinusoidal, achieving balance may be troublesome, since harmonics may disturb the balance condition. The use of filters with the null detector in such cases may solve the problem.

Note:-

The inductance of an inductive coil is generally measured by the usual inductive circuit like Maxwell-Wein Bridge, Hay Bridge, Anderson’s bridge, Owen’s Bridge

The Anderson’s bridge gives an accurate measurement of the self-inductance of the circuit.

De-Sauty’s Bridge is used to measure the value of unknown capacitance in terms of standard capacitance.