Correct Answer - Option 3 : 200
Range settings of resistance meter are:
200 Ω, 2 kΩ, 20 kΩ, 200 kΩ, 2 MΩ.
Full scale voltage = 2 Vs
Maximum full-scale current rating in individual range are,
\(200\;{\rm{\Omega }}\;range:I = \frac{2}{{200}} = 10mA\)
2 kΩ range: I = 1 mA = 1000 μA
20 kΩ range: I = 100 μA
200 kΩ range: I = 10 μA
2 MΩ range: I = 1 μA
Rating of device = 100 μW, 8 kΩ - 12 kΩ
Current rating corresponding to 8 kΩ is
\({I^2} = \frac{{100 \times {{10}^{ - 6}}}}{{8 \times {{10}^3}}} \Rightarrow I = 0.1118\;mA\)
= 111.8 μA
Current rating corresponding to 12 kΩ is,
\({I^2} = \frac{{100 \times {{10}^{ - 6}}}}{{12 \times {{10}^3}}} \Rightarrow I = 91.28\mu A\)
The resistance of device is 8 kΩ - 12 kΩ
The selected range should be more than this rating.
So, 20 kΩ, 200 kΩ and 2 MΩ are the options.
The range near to 12 kΩ is 20 kΩ.
If we select 20 kΩ range,
The current rating is 100 μA and it is greater than device current rating 91.28 μA.
So, it is unsafe to choose 20 kΩ range.
Next closest range is 200 kΩ.
The current rating in this case is 10 μA and it is much lower than the device current rating and it is safe for the device.
So, the best resolution is possible for 200 kΩ.
Note: Best resolution is possible for lower range values.
