Measuring instruments, earthing and safety notes — Unit 5

Electrical measuring instruments are used to detect or measure electrical quantities like current, voltage, power, and energy. Based on their accuracy and calibration, they are broadly classified into two categories:

• Absolute Instruments: Give the value of the electrical quantity in terms of the instrument's physical constants (e.g., Tangent Galvanometer). They don't need calibration but are too slow and bulky for daily use. Mostly used in labs for standardizing.
• Secondary Instruments: The deflection gives the electrical quantity directly (e.g., Ammeters, Voltmeters). They must be calibrated against an absolute instrument. Used in all practical applications.

Secondary instruments are further classified based on how they display the measured quantity:

• Indicating Instruments: Indicate the instantaneous value via a pointer moving over a calibrated scale (e.g., Ammeter, Voltmeter).
• Recording Instruments: Continuously record the variations of the quantity over time on a moving paper chart (e.g., ECG machine, substation voltage recorders).
• Integrating Instruments: Measure the TOTAL quantity of electricity or energy consumed over a period of time (e.g., Energy meter in your house).

For any indicating instrument (pointer type) to work accurately and stably, three distinct torques must act on its moving system:

• 1. Deflecting Torque ($T_d$): Forces the pointer to move from the zero position.
• 2. Controlling Torque ($T_c$): Opposes the deflecting torque and brings the pointer to rest at a steady final position.
• 3. Damping Torque: Prevents the pointer from oscillating around the final reading, ensuring it settles quickly.

This is the driving force. It is produced by utilizing various effects of electric current:

• Magnetic Effect: Used in Moving Iron and PMMC ammeters/voltmeters.
• Heating Effect: Used in thermal instruments (Hot wire).
• Electrostatic Effect: Used in Electrostatic voltmeters.
• Electromagnetic Induction: Used in AC energy meters.

The magnitude of the deflecting torque is directly related to the magnitude of the electrical quantity being measured ($T_d \propto I$ or $T_d \propto I^2$).

Without controlling torque, any small deflecting torque would push the pointer completely off the scale. $T_c$ increases as the pointer deflects further.

The pointer comes to rest precisely when $T_d = T_c$.

⇒Methods of providing Control:

• Spring Control: Two phosphor-bronze hairsprings attached to the spindle. As it turns, they wind up, creating an opposing force. $T_c \propto \theta$ (deflection angle). Creates a UNIFORM scale.
• Gravity Control: A small weight is attached to the moving system. As it turns, gravity tries to pull it back down. $T_c \propto \sin\theta$. Creates a CRAMPED scale.

Because the moving system has inertia, when $T_d = T_c$, it will overshoot and oscillate back and forth like a pendulum before settling. Damping torque acts like "friction" that only exists when the pointer is moving, killing the oscillations.

⇒Methods of Damping:

• Air Friction Damping: A light aluminum piston attached to the spindle moves inside a closed air chamber.
• Fluid Friction Damping: Similar, but uses a high-viscosity oil instead of air.
• Eddy Current Damping: The most efficient. A metal disc on the spindle rotates between the poles of a permanent magnet. Eddy currents induced in the disc oppose the motion (Lenz's Law).

Permanent Magnet Moving Coil (PMMC) instruments are the most accurate and sensitive instruments, but they work ONLY for DC measurements.

⇒Construction

A rectangular coil of fine copper wire wound on a light aluminum frame. The frame is suspended between the poles of a strong, U-shaped permanent magnet.

• Control: Spring control (hairsprings).
• Damping: Eddy current damping (in the aluminum frame).

Principle: When a current-carrying coil is placed in a magnetic field, it experiences an electromagnetic torque. (Motor principle).

Force on one side of coil: F = N B I L
Torque = Force × perpendicular distance (width b)
T_d = (N B I L) × b
Since Area A = L × b:
T_d = N B A I
Let K_d = NBA (constant). So, T_d ∝ I

Since Spring Control is used ($T_c \propto \theta$), at equilibrium ($T_d = T_c$): $\theta \propto I$. This means PMMC instruments have a perfectly Uniform Scale.

MI instruments are incredibly robust and cheap. They can measure both AC and DC. They are the most commonly used ammeters and voltmeters in switchboards.

⇒Two Types:

• Attraction Type: A flat piece of soft iron is eccentrically pivoted outside a stationary coil. When current flows, the coil becomes a magnet and literally "attracts" the iron piece into it, moving the pointer.
• Repulsion Type: Two soft iron vanes (one fixed, one moving) are placed inside a stationary coil. Current magnetizes both with the SAME polarity. They repel each other, moving the pointer.

The magnetic field produced by the stationary coil is proportional to the current ($B \propto I$). The magnetization of the iron piece is also proportional to the field, hence to the current ($M \propto I$).

The force (and thus torque) is the product of the two: $F \propto B \times M \implies T_d \propto I \times I$.

T_d ∝ I²

Because torque is proportional to the square of the current, it is always positive regardless of current direction. This is why it measures AC! Also, at equilibrium ($T_d = T_c$), we get $\theta \propto I^2$. This results in a Non-Uniform (Cramped) Scale.

A basic PMMC galvanometer can only carry a few milliamperes. To measure large currents (e.g., 100 A), we must bypass the excess current around the meter.

⇒Using a Shunt

A Shunt is a very low resistance resistor connected in parallel with the ammeter. Most of the heavy line current bypasses through the shunt.

R_sh = R_m / (m - 1)

Where:
R_m = Internal resistance of meter
m = Multiplying factor = (Desired total Current / Full-scale meter Current)

A basic meter can only handle a few millivolts across its terminals before the delicate coil burns out. To measure large voltages, we must drop the excess voltage before it reaches the meter.

⇒Using a Multiplier

A Multiplier is a very high resistance resistor connected in series with the voltmeter. It absorbs most of the voltage drop.

R_se = R_m (m - 1)

Where:
R_m = Internal resistance of meter
m = Multiplying factor = (Desired total Voltage / Full-scale meter Voltage)

An electric shock occurs when the human body becomes part of an electrical circuit. The severity of a shock depends ENTIRELY on the amount of Current flowing through the body, not the voltage.

Dry human skin has high resistance ($\sim 100,000\,\Omega$), but wet skin drops to $\sim 1,000\,\Omega$. At 230V, $I = 230/1000 = 230$ mA, which is instantly lethal.

Earthing means connecting the non-current-carrying metallic parts of electrical appliances (like the metal body of a fridge) directly to the general mass of the Earth (which sits at 0V potential).

⇒Why is it necessary?

If insulation fails and a live wire touches the metal casing, the entire casing becomes 230V live. If a human touches it, fatal current flows through them to the ground.

If the casing is earthed, the thick earth wire provides a virtually zero-resistance path. The massive fault current bypasses the human entirely and goes straight to earth. This huge current also instantly blows the fuse, disconnecting the power safely.

⇒1. Pipe Earthing

The best and most common method. A galvanized iron (GI) pipe (approx. 38mm diameter, 2m length) with holes drilled in it is buried vertically in a deep pit. The pit is filled with alternate layers of charcoal and salt to maintain high moisture and low soil resistance.

⇒2. Plate Earthing

A copper or GI plate (e.g., $60\text{cm} \times 60\text{cm} \times 3.18\text{mm}$) is buried vertically in a pit 3 meters deep, also packed with charcoal and salt. A thick earth wire is bolted to it and brought up to the building.

A fuse is the simplest protective device. It is a short piece of wire with a low melting point (usually lead-tin alloy) inserted in series with the live wire.

⇒Working

When excess current (overload or short circuit) flows, the massive $I^2R$ heat generated melts the wire, breaking the circuit.

• Advantage: Extremely cheap, absolute fail-safe interruption.
• Disadvantage: Once blown, it is destroyed and must be manually replaced before power can be restored.

An MCB is an electromechanical switch that automatically opens (trips) under fault conditions. It replaces the traditional fuse in modern wiring.

⇒Working Mechanisms:

• Thermal Tripping (for Overload): A bimetallic strip heats up, bends, and unlatches a mechanical trip mechanism. This takes time, allowing temporary harmless surges (like motor starting).
• Magnetic Tripping (for Short Circuit): A small solenoid acts instantly. If a massive short-circuit current flows, the magnetic field instantly pulls a plunger, tripping the breaker in milliseconds.

After tripping, the MCB can simply be switched back ON manually.

Fuses and MCBs protect equipment from huge overcurrents (5A, 10A, 50A). They CANNOT protect humans from electrocution (which only takes 0.05A). For life safety, we use an ELCB or RCCB (Residual Current Circuit Breaker).

⇒Working Principle

Under normal conditions, Current flowing OUT through the Live wire must exactly equal Current returning IN through the Neutral wire. The net magnetic field in the RCCB sensing core is zero.

If a human touches the live wire, 30mA of current leaks through their body to the ground. Now, Live Current $\neq$ Neutral Current. This residual current creates a magnetic flux that trips the breaker instantly (within 30ms), saving the person's life.

⇒Unit 5 Mastery

• Why is damping torque necessary in indicating instruments?
• Derive the deflecting torque equation for PMMC and state why its scale is uniform.
• Compare PMMC and MI instruments (Scale, Damping, AC/DC use).
• Calculate the required shunt/multiplier resistance to extend a meter's range.
• Explain the difference between a fuse and an MCB.
• Draw a simple diagram for Pipe earthing and explain its necessity.
• How does an RCCB save human lives from electric shock?