SOLUTION

If the instrument has a wide range, the instrument should have a Logarithmic scale.

Various Scales for measurement through an instrument are

1. Linear Scales:- A linear scale like a foot rule, is the simplest to read. Though termed as linear it may form a part of the arc, however, the graduations will be uniformly disturbed. The moving coil electrodynamic wattmeters generally have a linear scale. Moving iron instruments also have nearly linear scales.

2. Square low scale:- Some instruments like thermal instruments, electrodynamic voltmeters, and ammeters follow the square law scale.

3. Logarithmic scale:-

• The logarithm and its use is nothing more than a mathematical tool that simplifies dealing with very large and very small numbers.
• For example, the logarithm of the number 1,000,000 is six, and the logarithm of the number 0.000001 is -six (minus six).
• Obviously, as more zeros are added before or after the decimal point, convening these numbers to their logarithms greatly simplifies calculations that use these numbers.
• If the current to be measured extends over a wide dynamic range, for example spanning several orders of magnitude, there is a risk that the signal conditioning circuit can saturate at its upper or lower limit and no measurement will be obtained.
• This problem can arise in the measurement of photocurrents in the atmosphere which span a large range of values during the daytime, and in atmospheric electricity measurements where currents generated in elevated points vary between HA in disturbed weather to pA in fair weather.
• An alternative approach for current measurement is therefore needed if, in preserving the capability to measure large currents, a good resolution is still required at the low current end of the range.
• A wide operating range can be achieved with a logarithmic current amplifier, which generates an output voltage proportional to the logarithm of the input current.
• This can be implemented with an opamp by using a device having an exponential voltage-current response in place of the feedback resistor of the trans-resistance configuration, such as a diode.
• Similarly, we use logarithmic scales for things that come in an extremely wide variety of sizes. Earthquakes are just one example: a 9.0 earthquake releases a trillion times as much energy as a 1.0 earthquake.
• If we used a linear scale, we would have to use giant numbers to describe earthquakes; for example, a 6.0 magnitude earthquake would be a 1,000,000,000 size earthquake, and a 9.0 magnitude earthquake would be described as a 1,000,000,000,000 size earthquake.