SSC JE Electrical Previous Year Question Paper 2018-SET 6

The dimension of energy is the same as that of work.

Finding the dimension of work:

Work = Force × Displacement

Force = Mass × Acceleration

Acceleration = Velocity/Time

Velocity = Distance/Time

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

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

⇒ 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] 

⇒ Work = Force × Displacement = [M L T ⁻²] × [L]

Work = [M L² T ⁻²] or [M L² ⁄ T²]

Moving – Iron (M.l.) Ammeters and Voltmeters

This type of instrument is principally used for the measurement of alternating currents and voltages, though it can also be used for d.c. measurements. There are two types of moving-iron instruments.

(i) Attraction type in which a single soft-iron vane (or moving iron) is mounted on the spindle and is attracted towards the coil when operating current flows through it.

(ii) Repulsion type in which two soft-iron vanes are used; one fixed and attached to the stationary coil while the other is movable (i.e. moving iron) and mounted on the spindle of the instrument. When operating current flows through the coil, the two vanes are magnetized, developing similar polarity at the same ends. Consequently, repulsion takes place between the vanes and the movable vane causes the pointer to move over the scale.

Attraction Type Instrument

Construction

The sectional view of an attraction-type moving iron instrument is shown in Figures  It consists of a stationary hollow cylindrical coil. An oval-shaped soft iron piece is mounted eccentrically to the spindle to which a pointer (needle) is attached. The controlling torque is provided by spring control method while damping torque is provided by air friction, as shown in Figures

Working of Attraction Type. When the instrument is connected to the circuit to measure current or voltage, the operating current flowing through the coil sets up a magnetic field. In other words, the coil behaves like a magnet and therefore it attracts the soft-iron piece towards it. The result is that the pointer attached to the moving system moves from zero position. The pointer will come to rest at a position where deflecting torque is equal to the controlling torque. If the current in the coil is reversed, the direction of the magnetic field also reverses and so does the magnetism produced in the soft-iron piece. Hence, the direction of the deflecting torque remains unchanged. For this reason, such instruments can be used for both d.c. and a.c. measurements.

Deflecting torque:- Torque in the attraction-type moving-iron instrument, the deflecting torque is due to the force of attraction between the field of the coil and the moving iron disc.

The magnetization of the iron disc or pole strength is proportional to the magnetic field strength H. The force F pulling the disc inwards is proportional to the Pole strength M of the disc and field strength H.

Therefore the deflecting torque

T_d ∝ MH

M ∝ H

H ∝ I

T_d ∝ I²

Hence the deflecting torque depends on the attraction between the field of the coil and the moving iron disc. That is, in an ammeter, the torque is roughly proportional to the current squared. The instrument, therefore, has the square-law response. The deflection is proportional to the mean value of the square of the current. When used on AC, it indicates the RMS or effective value of current (or voltage).

Controlling Torque:-  In this type of instrument, controlling torque is obtained by either with a spring or by gravity. In Fig. a spring has been used for the controlling torque.

Damping Torque:- In this type of instrument, pneumatic type damping is used. Eddy currents cannot be employed because the presence of a permanent magnet, required for such a purpose, would affect the deflection and hence the reading of the instrument.

As the deflection torque, in both attraction and repulsion-type moving-iron instruments, is proportional to the square of the current, the scale is crowded (not uniform) at the beginning. It is more so with the gravity control as the controlling torque is proportional to the sine of the angle of deflection, i.e. sine θ. This is rectified to some extent by making the moving vanes of a suitable shape.

Advantages of Moving Iron Instrument

• Moving iron instruments are the cheapest elements and are robustly used in industry.
• Usable in both a.c. and d.c. circuits.
• They are simple in construction
• They possess high operating torque and can withstand overload momentarily.

Disadvantages of Moving Iron Instrument

• Have a non-linear scale.
• Cannot be calibrated with a high degree of precision for d.c. on account of the effect of hysteresis in the iron vanes.
• Deflection of up to 240° only may be obtained with this instrument.
• The instrument will always have to be put in the vertical position if it uses gravity control.
• High power consumption and poor sensitivity
• Change in frequency introduces errors and these cannot be calibrated with the high degree of Precision

A multimeter, also known as a VOM (Volt-Ohm-Milliammeter) is a combination of a voltmeter, ohmmeter, and a current meter. it 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 form. Although analog multimeters are being replaced by digital multimeters.

Note:-  Power can be measured by measuring the voltage and current in a circuit and finding the product of the two. A single meter that indicates power in the circuit is called a wattmeter.

Permanent Magnets Moving Coil “PMMC” Instrument 

These instruments are used either as ammeters or voltmeters and are suitable for d.c. work only. This type of instrument is based on the principle that when a current-carrying conductor is placed in a magnetic field, the mechanical force acts on the conductor. The coil placed in the magnetic field and carrying the operating current is attached to the moving system. With the movement of the coil, the pointer moves over the scale to indicate the electrical quantity being measured. This type of movement is known as the D’Arsonval movement.

Errors In PMMC Instrument

The basic sources of errors in PMMC instruments are friction, temperature, and aging of various parts. To reduce the frictional errors ratio of torque to weight is made very high.

The most serious errors are produced by the heat generated or by changes in the temperature. This changes the resistance of the working coil, causing large errors. In the case of voltmeters, a large series resistance of a very low-temperature coefficient is used. This reduces the temperature errors.

The aging of permanent magnet and control springs also causes errors. The weakening of the magnet and springs cause opposite errors. The weakening of the magnet causes less deflection while the weakening of the control springs causes large deflection, for a particular value of current. The proper use of material and pre-aging during manufacturing can reduce tt errors demo the weakening of the control spring.

Hay’s bridge is a modification of Maxwell’s bridge. This method of measurement is particularly suited for high Q inductors.

The unknown inductor L_X of effective resistance R_X is compared with the standard known variable capacitor C₄. This bridge uses a resistance R₄ in series with the standard capacitor C₄ (unlike in Maxwell’s bride where R₄ was in parallel with C₄). The other resistances R₂ and R₃ are known as no-inductive resistors.

The quality factor of the Hay bridges is given as

Q = ωL_x ⁄ R_x = 1 ⁄ ωC₄R₄

where ω = 2πf = 2 × 3.14 × 50 = 314

Q = 1 ⁄ ωC₄R₄ = 1 ⁄ 314 × 40 × 10⁻⁶ × 40

Q = 2

We can determine the relation between apparent power and reactive power by the power triangle

Reactive Power in an A.C circuit is given as

Q = V.I.Sinθ

or

V.I = Q/Sinθ———-(1)

Apparent power in an A.C circuit is

S = V.I

or

S = Q/Sinθ——-(From equation 1)

Power factor cosφ = 0.8

cosφ = 0.8

Sin²φ = 1 − cos²φ

Sin²φ = 1 − (0.8)²

Sinφ = 0.6

S = 60/0.6

S = 10 watt

Energy consumption or power consumption refers to the electrical energy per unit time is given as

Energy consumption = Power × Time

(i) Since the building has 3 floors and each floor has 4 fans of 50 W that operates for 12 hours

3 × 4 × 50 × 12 × 30 = 216000 Watt.hr

One air conditioner working for 2 hours per day

1 × 3000 × 2 × 30 = 180000 Watt.hr

Total energy consumption

216000 + 180000 = 396000 watt-hr

= 396 kWh

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

Total Power = W₁ + W₂

And

W₁ = W₂

Total Power = 6 kW

∴ W₁ = 3kW

&

W₂ = 3kW

System voltage i.e Nominal voltage = 11000 V

Transformation ratio of the potential transformer is

V₁/V₂ = N₁/N₂

V₁/V₂ = 108

Primary voltage = Turn ratio × Secondary voltage = V₂ × 104 = 108V₂

Percentage of error is the Potential error

= (Nominal voltage − Primary voltage)/Primary voltage

5% = (11000 − 108V₂)/108V₂

1/20 = (11000 − 108V₂)/108V₂

108V₂ = 220000 − 2160V₂

2268V₂ = 220000

V₂  = 97 V

The sensitivity of a voltmeter is given in ohms per volt. It is determined by dividing the sum of the Internal resistance of the meter (R_m) plus the series resistance (R_s), by the full-scale reading in volts. In equation form, sensitivity is expressed as follows:

Sensitivity (S) = (R_m + R_s) ⁄ V_fld

or

V_fld = (R_m + R_s) × S

= (230 + 70) × 3

V_fld = 100 kV