Basics of Electrical Instruments

 A (0-1)mA linear instrument with an internal resistance of 100Ω is to be converted into a (0-10)V voltmeter.

Without any limiting series resistor, a circuit may damage if there is an excess flow of 0.1 A in a 1mA ammeter(linear instrument). 

It is a series circuit where Rse should be in order to limit the flow of current in the ammeter so that it won't damage.

So we add Rse in series with the internal resistance.

Therefore we get,

Current should not cross the full-scale value anytime that's why we include series resistance.

After doing so we need to put calibration for scaling the voltmeter range.

Equivalent circuits of voltmeter:

Here the current is the same in the circuit so we put the equation as,

In the circuit, Im is the full-scale deflection current.

m = multiplication factor

We can find the Rse using this formula.

The multiplication factor is one where it is used for calibration.

From a linear instrument if we need to design a voltmeter then we need to increase the Rse value in order to increase the voltmeter range.

A (0-1)mA linear instrument with an internal resistance of 100Ω is to be converted into a (0-10)A ammeter.

Now Rse cannot be included in the circuit to limit the current as the current is the same in the series circuit.

Because of the direct flow of 10A current in the series circuit, the ammeter may damage.

So we have to connect the shunt resistance in order to limit the current.

Therefore the equivalent circuit of an ammeter is,

Equivalent circuit of an ammeter:

To find Rsh, we apply the current division rule so we get,

The voltage drop will be the same in the circuit so the equation will be as,

m= multiplication factor

We can also find the shunt resistance using this simple formula. Without applying the current division rule.

Basics of Electrical instruments:

The electrical instruments in measurements convert energy from one form to the other.

In general, it is converted from electrical energy to mechanical energy.

The electrical instruments deal with motoring action when we supply current where the pointer moves which shows deflection. We need to stop this pointer at a certain level when we give current so we need some force that has to act opposite so that it will stop at the required reading. For this, the deflection torque should be related to the opposite torque so that according to the input the force acts in an opposite direction.

We have three torques in an electrical instrument or meter namely:

• Deflection torque 
• Controlling torque
• Damping torque

Deflection torque:

Initially, when there is a current flow in an instrument some force or torque will be developed on the pointer because of this force the pointer rotates continuously.

Controlling torque:

We need to stop the pointer so that the opposite force acts on it which is done by the controlling force or torque.

When both forces act on each the pointer will come to the steady-state where some of the oscillations will be developed.

Damping force:

In order to reduce the number of oscillations of the pointer at a steady-state, we use one more force which is a damping force.

Controlling torque using a controlling system:

The electrical instruments, in the controlling torque, are created by Spring control or by using gravity control.

i) Spring control:

Spring control has two pivots, jewel bearings to reduce the friction, a spring that is made up of phosphor bronze, and a pointer that is connected to the spindle so that when the spindle rotates the pointer moves.

Whenever we supply a voltage then there will be a current flow in the meter and the force will get developed(when a current-carrying conductor is placed in a magnetic field it experiences a force) so that the pointer moves and we get a deflection. Ultimately this deflection torque is related to the controlling torque and damping force. In this spring control system, the pointer is connected to the spring so that when there is a movement of the pointer spring stores energy upon compression. Therefore this spring tries to release the stored energy hence some opposite force is developed on the deflection torque at this state the deflection torque is equal to the controlling torque.

When Td = Tc, before reaching the steady-state there will be a lot of oscillations.

    θ ∝ Td

    Tc  ∝ θ 

Tc  = Kc θ 

Where Kc is Spring constant,

At one instant, the controlling torque is proportional to the deflection torque

Advantages of Spring control:

• Accuracy is high because of its linear relationship.
• It is possible to place the meter horizontal as well as vertical.

Disadvantages of spring control:

• Aging effect - Due to the elasticity property in the spring there will be an aging effect after several usages.
• Temperature error

ii) Gravity control technique:

In this instrument, we have two balancing weights. Whenever there is a flow of current the force will be developed and there will be a deflection as the pointer moves. Immediately the W2 weight attached to the pointer also moves which opposes the deflection torque due to the gravitational force.

When there is no current flow then the W2 comes back to its initial position so that the pointer will also be back to the null deflection.

Advantages of Gravity control:

There is no aging effect and there is no temperature error.

Disadvantages of Gravity control:

This meter has to be operated horizontally as it works based on the gravitational force.

Damping force mechanism:

• Air friction damping
• Fluid friction damping 
• Eddy current damping

Air friction damping:

As Tc = Td, there will be oscillations developed. In order to reduce this oscillation, it is a mandatory thing to reduce the speed of the pointer.

The pointer moves at high speed because of the current flow, thereby to make a pointer smooth move there is a need for another force which is a damping force. 

This force can be achieved by using air friction damping.

There is a cylinder, a piston, and the air is filled in the cylinder in the air friction damping.

In air friction damping, the piston is connected to the spindle, when the spindle rotates the piston moves in the cylinder and it will develop an air pressure which in turn it tries to push the piston back. Because of this pressure, the pointer experiences a smooth force.

Fluid friction damping:

It works in the same process as to how the air friction works but the change here is the fluid where we replace fluid instead of air.

Since the fluid has the property of viscosity it is more effective but it needs regular maintenance.

Eddy current damping:

It is the more effective damping compared to air friction damping and fluid friction damping.

In this damping, there is a permanent magnet and an aluminum disc.

Whenever there is a current flow, the deflection torque is produced and the aluminum disc is attached to the spindle where it cuts the flux lines on the permanent magnet so that an emf is generated thereby an eddy current is developed on the aluminum disc. This eddy current opposes the spindle so that it reduces the number of oscillations of the pointer and reduces the settling time.