MI Instruments MCQ Quiz - Objective Question with Answer for MI Instruments - Download Free PDF

Concept

The impedance for the series RL circuit is given by:

\(Z=\sqrt{R^2+X_L^2}\)

where, Z = Impedance

R = Resistance

X_L = Reactance

Calculation

Given, R = 4000Ω

V_DC = 200 V

V_AC = 200 V

I_AC = 0.04A

AC impedance, \(Z={V_{AC}\over I_{AC}}\)

\(Z={200\over 0.04}=5000\space \Omega\)

Since the impedance is higher than the DC resistance, it suggests the presence of an inductive reactance X_L.

\(5000=\sqrt{(4000)^2+X_L^2}\)

XL = 3000 Ω

A moving iron voltmeter measures the RMS voltage but is calibrated based on the assumption of pure resistance. The actual voltage it registers is:

V_read = I_AC × R

Vread = 0.04 × 4000 

Vread = 160 V

% error = \({V_{true}-V_{read}\over V_{true}}\times 100\)

% error = \({200-160\over 200}\times 100\)

% error = 20%

Explanation:

Moving Iron Instrument

Definition: A moving iron instrument is an electrical measurement device used to measure both alternating current (AC) and direct current (DC). It operates on the principle of electromagnetic force, where a piece of iron moves in response to the magnetic field produced by the current flowing through a coil.

Working Principle: The moving iron instrument consists of a coil and a piece of soft iron. When current flows through the coil, it generates a magnetic field. The magnetic field induces a force on the iron piece, causing it to move. The movement is proportional to the strength of the current, and this movement is indicated on a calibrated scale. There are two main types of moving iron instruments: attraction type and repulsion type.

Attraction Type: In this type, the iron piece is attracted towards the coil when current flows through it. The movement of the iron is proportional to the square of the current.

Repulsion Type: In this type, two pieces of iron are placed such that when current flows through the coil, both pieces are magnetized with the same polarity and repel each other. The repulsion causes a movement that is also proportional to the square of the current.

Advantages:

• Can measure both AC and DC currents accurately.
• Rugged and robust construction, making them durable and suitable for industrial environments.
• Relatively simple design and low cost.

Disadvantages:

• Non-linear scale, especially at the lower end, due to the square law response.
• Less sensitive compared to moving coil instruments.
• Prone to errors due to hysteresis and eddy currents in the iron parts.

Applications: Moving iron instruments are commonly used in industrial and laboratory settings for measuring AC and DC currents and voltages. They are particularly useful in applications where ruggedness and the ability to measure both types of currents are required.

Correct Option Analysis:

The correct option is:

Option 2: AC as well as DC current.

This option correctly describes the capability of moving iron instruments. They are designed to measure both alternating and direct currents, which is a significant advantage in various practical applications. The iron piece in the instrument responds to the magnetic field generated by the current, whether it is AC or DC.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Only AC current.

This option is incorrect because moving iron instruments can measure both AC and DC currents. While they are effective for AC measurements due to their ability to respond to the magnetic field generated by the alternating current, they are equally capable of measuring DC current.

Option 3: Only DC current.

This option is also incorrect because it limits the functionality of moving iron instruments to DC measurement only. As previously explained, these instruments can measure both AC and DC currents due to their design and operational principle.

Option 4: Only heat.

This option is entirely incorrect as moving iron instruments are designed to measure electrical current, not heat. The instrument operates based on the electromagnetic force exerted on the iron piece by the magnetic field of the current, and heat measurement is not within its scope of functionality.

Conclusion:

Understanding the operational principles and capabilities of moving iron instruments is crucial for their effective application. These instruments offer the versatility to measure both AC and DC currents, making them valuable tools in various electrical measurement scenarios. Their rugged design and ability to handle different types of current flow enhance their utility in industrial and laboratory environments, despite some limitations such as non-linearity and sensitivity issues.

Concept

The voltage reading of a moving iron voltmeter corresponds to the true RMS voltage across its resistance:

V_meter = I_AC × R

where, I_AC = AC current

R = DC resistance

Calculation

Given, V_DC = 250 V

I_DC = 0.05 A

L = 1 H

f = 100 Hz

Impedance at 100Hz, Z_AC = 6000 Ω

\(R={V_{DC}\over I_{DC}}\)

\(R={250\over 0.05}=5000\space Ω\)

\(Z_{AC}=\sqrt{(R)^2+(X_L)^2}\)

\(X_L=2\pi fL=2\pi (1000)(1)=628.32\space Ω\)

\(Z_{AC}=\sqrt{(5000)^2+(628.32)^2}\)

Z_AC = 5040 Ω 

\(I_{AC}={V_{AC}\over Z_{AC}}\)

\(I_{AC}={250\over 6000}=0.04167A\)

Vmeter = (0.04167) × (5000)

Vmeter = 208.33 V

Concept

The deflecting torque in the MI instrument is given by:

\(T_d={1\over 2}I^2{dL\over dθ}\)

The controlling torque in the MI instrument is given by:

\(T=kθ\)

At equilibrium: TC = T_d

\(kθ={1\over 2}I^2{dL\over dθ}\)

\(θ={I^2\over 2k}{dL\over dθ}\)

Calculation

Given, I = 5 A

k = 12 × 10-6 Nm/rad

L = (10 + 5θ - θ2) μH

\({dL\over dθ}=(5-2θ)\times 10^{-6}\)

\(θ={5^2\over 2\times 12\times 10^{-6}}\times(5-2θ)\times 10^{-6}\)

θ = 1,689 radians

To convert in degrees, multiply by 180°/π 

θ = 96.8 degree

Extension of PMMC as an ammeter

The range of a moving iron ammeter can be extended by using a low value of shunt resistance connected in parallel with an ammeter.

The value of shunt resistance is given by:

\(R_{sh}={R_m\over ({m}-1)}\)

In order to operate meter at all frequencies, time constant of both branches must be equal.

\(τ_{sh}=τ_{m}\)

Calculation

Given, \(R=50\space m\Omega\)

\(m={10\over 1}=10\)

\(R_{sh}={50\over (10-1)}\)

R_sh = 5.55 mΩ

\(τ_{sh}=τ_{m}={L_m\over R_m}\)

\(τ_{m}={0.1\over 50}=2\space sec\)

NOTE

In official paper answer was given 2 milliseconds but actually according to given values answer is coming to be 2 seconds,. So we have chosen the most appropriate answer as option (C) which matches the official answer key.

• The instruments which use the heating or thermal effect of the current for knowing their magnitude such type of instrument is known as the hot wire instrument.
• The hot wire instrument is used for both the AC and DC current.
• Hotwire instrument works on the principle of the thermal effect, that the length of the wire increases because of the heating effect of the current flow through it.
• When the current is passed through the fine platinum-iridium wire it gets heated up and expands.
• The sag of the wire is magnified, and the expansion is taken up by the spring.
• This expansion causes the pointer to deflect, indicating the value of the current.
• This expansion is directly proportional to the heating effect of the current and hence directly proportional to the square of the RMS value of the current.
• Therefore, the meter may be calibrated to read the rms value of the current.​

Moving iron instrument

The instrument in which the moving iron is used for measuring the flow of current or voltage is known as the moving iron instrument. It works on the principle that the iron placed near the magnet attracts it.

The force of attraction depends on the strength of the magnet field. The magnetic field induces by the electromagnet whose strength depends on the magnitude of the current that passes through it.

Characteristics of MI instruments

1. It has a non-uniform scale
2. The controlling torque is provided by spring control.
3. The damping torque is provided by air friction damping.

Advantages of MI instruments

1. ​It can work on AC and DC both.
2. Less frictional error
3. It can be used under severe overload conditions. 

​Disadvantages of MI instruments

1. It cannot be used at high frequencies due to the saturation of the magnetic core.
2. Some serious error occurs in the instruments because of the hysteresis, frequency, and stray magnetic field.
3. In the MI instrument, the deflection torque is  directly proportional to the square of the current. Because of this, the waveform error occurs in the instrument.

Concept:

In moving iron instruments, the deflecting torque is unidirectional (acts in the same direction) whatever may be the polarity of the current.

The deflecting torque is given by

\({T_d} = {I^2}\frac{{dL}}{{dθ }}\)

Where,

I is operating current

L is self-inductance

θ is deflection

\({T_d}\propto {I^2}\)

So that the deflection torque of the moving iron instrument is proportional to the square of the RMS value of the operating current and change in self-inductance. 

Calculation:

When the current through a moving iron instrument is increased by 20%, then deflection torque is

\({T'_d}\propto {{(1.2I)}^2}\)

∴ T'_d = 1.44 T_d

Hence deflection torque is increased by 44%

The correct answer is both DC and AC.

Explanation:

Moving iron instrument

The instrument in which the moving iron is used for measuring the flow of current or voltage is known as the moving iron instrument. It works on the principle that the iron placed near the magnet attracts it.

The force of attraction depends on the strength of the magnet field. The magnetic field induces by the electromagnet whose strength depends on the magnitude of the current that passes through it.

Characteristics of MI instruments

1. It has a non-uniform scale
2. The controlling torque is provided by spring control.
3. The damping torque is provided by air friction damping.

Advantages of MI instruments

1. ​It can work on AC and DC both.
2. Less frictional error
3. It can be used under severe overload conditions. 

​Disadvantages of MI instruments

1. It cannot be used at high frequencies due to the saturation of the magnetic core.
2. Some serious error occurs in the instruments because of the hysteresis, frequency, and stray magnetic field.
3. In the MI instrument, the deflection torque is not directly proportional to the square of the current. Because of this, the waveform error occurs in the instrument.

Concept:

The defecting torque is given by

\(T_d = \frac{{{I^2}}}{2}\frac{{dL}}{{d\theta }}\)

The deflection angle in a moving iron instrument is given by

\(\theta = \frac{1}{{{K_c}}}\frac{{{I^2}}}{2}\frac{{dL}}{{d\theta }}\)

I is the current flows through the coil

Kc is the spring constant

\(\frac{{dL}}{{d\theta }}\) is the change in self-inductance of a coil with change in the deflection angle.

Calculation:

Given that, I = 20 A

Deflecting torque (T_d) = 6 × 10^-5 N-m

\( \Rightarrow 6 \times {10^{ - 5}} = \frac{{{{(20})^2}}}{2}\frac{{dL}}{{d\theta }}\)

\( \Rightarrow \frac{{dL}}{{d\theta }} = 0.3\;\mu H/rad\)

Concept:

Moving iron ammeter:

Moving iron ammeter is used to measure both AC and DC values in the circuit.

The reading of the MI instrument is in RMS value.

Calculation:

Moving iron ammeter reads the RMS value of alternating current.

The peak value of the waveform = I_m = 150 A

For rectangular waveform, RMS value (I₁)= peak value

I₁ = I_m = 150 A

For a sinusoidal waveform, the RMS value  of the current = I_m / √2

 \(I_2 = \frac{{150}}{{√ 2 }} = 106.6\;A\)

Points to remember:

• The PMMC instruments measure the quantity in DC only.
• The reading of the PMMC instruments is an average value.
• For alternative quantities, PMMC shows zero reading as it is not working on AC circuits

Moving iron (MI) instruments always measures the RMS value of a given quantity.

RMS (Root mean square) value:

• RMS value is based on the heating effect of wave-forms.
• The value at which the heat dissipated in AC circuit is the same as the heat dissipated in DC circuit is called RMS value provided, both the AC and DC circuits have equal value of resistance and are operated at the same time.

Calculation:

Given:

Current = i(t) = (18 + 10 sin ωt + 7 sin 2ωt)

RMS value of current = \( \sqrt {{{18}^2} + (\frac{{{10}}}{\sqrt2})^2 +( \frac{{{7}}}{\sqrt2}}) ^2\) = 19.962 A ≈ 20 A

Important Points

• Moving coil instrument (PMMC) always measures the average value of the signal provided.
• PMMC instruments are suitable for measuring only DC quantities whereas MI instruments are suitable for measuring both AC and DC quantities.

Concept:

Operating torque:

In moving iron instruments, the deflecting torque is given by

\(\Rightarrow \theta = \dfrac{1}{2}\dfrac{{{I^2}}}{{{K_c}}}\dfrac{{dL}}{{d\theta }}\)

I is the operating current in Ampere

L is the inductance in Henry

θ is the deflection angle in radians

Deflection is directly proportional to the square of the RMS value of the operating current. Hence, this instrument possesses high operating torque.

Calculation:

\(\begin{array}{l} L = \left( {20 + 4\;\theta } \right)\;\mu H\\ \frac{{dL}}{{d\theta }} = 4\;\mu H/rad \end{array}\)

\(\begin{array}{l} \theta = \frac{1}{2}\frac{{{I^2}}}{{{K_c}}}\frac{{dL}}{{d\theta }}\\ \theta = \frac{1}{2} \times \frac{{{{\left( 5 \right)}^2}}}{{10 \times {{10}^{ - 6}}}} \times \left( 4 \right) \times {10^{ - 6}}\\ \Rightarrow \;\theta = 5\;rad \end{array}\)

Moving iron voltmeter

• MI instrument is used to measure the RMS values.
• These instruments have a non-uniform scale.
• It works on the principle of attraction of a single piece of soft iron into the magnetic field.
• In the MI instrument, when the current is passed through the solenoid, a magnetic field is set up inside the solenoid. Then the iron piece gets magnetized which in turn deflects the pointer. 
• The deflecting torque produced is directly proportional to the square of the current.
• The controlling torque is provided by the spring control.
• The damping torque is provided by air friction damping.

Cathode ray oscilloscope (CRO)

CRO is used for the measurement of voltage, current, frequency, and phase angle of any electrical quantity.

Cathode ray oscilloscopes are suitable for the measurement of very low voltages at high frequencies. CRO is suitable for the measurement of 10 mV at 50 MHz.

Capacitive voltage transformer (CVT)

CVTs are primarily used for voltage measurement, providing voltage signals to metering units, protection relay devices, and automatic control devices. 

Instrument transformer

Instrument transformers are high-accuracy electrical devices used to isolate or transform voltage or current levels.