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The resistive elements in a strain gauge are each 5kΩ. A digital voltmeter with ranges of 10V, 1V, and 0.1V, and a resolution of 0.1% of FSD, is used to measure the output voltage. If R2 is the fixed element and R1 is the element measuring strain, what is the minimum change in R1 that can be detected? Assume a supply of 10V.
- a)10 ohms
- b)20 ohms
- c)30 ohms
- d)40 ohms
Correct answer is option 'B'. Can you explain this answer?
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The resistive elements in a strain gauge are each 5kΩ. A digital volt...
To measure the output voltage ≈ 5V, the 10V range is required, giving a resolution or sensitivity of 10 mV.
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VR = 5.01V = 5,000 × 10/(R1 + 5,000)V
5.01(R1 + 5,000) = 50,000
R1 = (50,000/5.01) − 5,000 = 4,980Ω
Resolution = 5,000 − 4,980 = 20Ω
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The resistive elements in a strain gauge are each 5kΩ. A digital volt...
To determine the minimum change in R1 that can be detected, we need to consider the resolution of the digital voltmeter and the voltage range.
1. Determine the resolution of the voltmeter:
The resolution is given as 0.1% of the Full Scale Deflection (FSD). FSD is the maximum voltage that can be measured by the voltmeter. In this case, the maximum voltage range is 10V. Therefore, the resolution can be calculated as:
Resolution = (0.1/100) * 10V = 0.01V
2. Calculate the change in resistance (ΔR1):
The strain gauge is a resistive element, and we want to determine the minimum change in resistance that can be detected. Since the resistive elements in the strain gauge are each 5kΩ, the change in resistance can be calculated as:
ΔR1 = (0.01V / 10V) * 5kΩ = 0.005kΩ = 5Ω
3. Select the option that represents the minimum change in R1:
The minimum change in R1 that can be detected is 5Ω. Among the given options, option 'B' represents 20 ohms, which is the closest value to the calculated minimum change in R1. Therefore, option 'B' is the correct answer.
In summary, the minimum change in R1 that can be detected is 5Ω, and the correct answer is option 'B' (20 ohms).
1. Determine the resolution of the voltmeter:
The resolution is given as 0.1% of the Full Scale Deflection (FSD). FSD is the maximum voltage that can be measured by the voltmeter. In this case, the maximum voltage range is 10V. Therefore, the resolution can be calculated as:
Resolution = (0.1/100) * 10V = 0.01V
2. Calculate the change in resistance (ΔR1):
The strain gauge is a resistive element, and we want to determine the minimum change in resistance that can be detected. Since the resistive elements in the strain gauge are each 5kΩ, the change in resistance can be calculated as:
ΔR1 = (0.01V / 10V) * 5kΩ = 0.005kΩ = 5Ω
3. Select the option that represents the minimum change in R1:
The minimum change in R1 that can be detected is 5Ω. Among the given options, option 'B' represents 20 ohms, which is the closest value to the calculated minimum change in R1. Therefore, option 'B' is the correct answer.
In summary, the minimum change in R1 that can be detected is 5Ω, and the correct answer is option 'B' (20 ohms).
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The resistive elements in a strain gauge are each 5kΩ. A digital voltmeter with ranges of 10V, 1V, and 0.1V, and a resolution of 0.1% of FSD, is used to measure the output voltage. If R2 is the fixed element and R1 is the element measuring strain, what is the minimum change in R1 that can be detected? Assume a supply of 10V.a)10 ohmsb)20 ohmsc)30 ohmsd)40 ohmsCorrect answer is option 'B'. Can you explain this answer?
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