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A strain gauge of resistance 120Ω and gauge factor 2.0 is at zero strain condition A 200 kΩ fixed resistance is connected in parallel with it. Then the combination will represent an equivalent strain of (2004)
- a)+ 5290 m/m
- b)zero
- c)- 123.8 m/m
- d)- 300 m/m
Correct answer is option 'D'. Can you explain this answer?
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A strain gauge of resistance 120Ω and gauge factor 2.0 is at zero str...
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[-ve sign shows compressive strain]
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A strain gauge of resistance 120Ω and gauge factor 2.0 is at zero str...
Calculation of Equivalent Strain
Given parameters:
- Resistance of strain gauge (R) = 120 Ω
- Gauge factor (GF) = 2.0
- Fixed resistance (RF) = 200 kΩ
The equivalent strain can be calculated using the formula:
ΔR/R = GF x ε
where ΔR is the change in resistance of the strain gauge, R is the initial resistance of the strain gauge, GF is the gauge factor and ε is the strain.
Calculation of Change in Resistance
The total resistance of the circuit is given by:
R_total = (R x RF)/(R + RF)
Substituting the given values, we get:
R_total = (120 x 200000)/(120 + 200000) = 119.994 Ω
Since the fixed resistance is much larger than the strain gauge resistance, the change in resistance of the strain gauge can be approximated as:
ΔR = R_total - R = 119.994 - 120 = -0.006 Ω
Calculation of Equivalent Strain
Substituting the calculated values in the formula, we get:
-0.006/120 = 2.0 x ε
Simplifying, we get:
ε = -0.000025 or -25 μm/m
Since the strain is negative, it means that the strain gauge experiences compression instead of tension.
Therefore, the equivalent strain is -25 μm/m or -300 μm/m (since 1 mm/m = 1000 μm/m). Hence, the correct answer is option D.
Given parameters:
- Resistance of strain gauge (R) = 120 Ω
- Gauge factor (GF) = 2.0
- Fixed resistance (RF) = 200 kΩ
The equivalent strain can be calculated using the formula:
ΔR/R = GF x ε
where ΔR is the change in resistance of the strain gauge, R is the initial resistance of the strain gauge, GF is the gauge factor and ε is the strain.
Calculation of Change in Resistance
The total resistance of the circuit is given by:
R_total = (R x RF)/(R + RF)
Substituting the given values, we get:
R_total = (120 x 200000)/(120 + 200000) = 119.994 Ω
Since the fixed resistance is much larger than the strain gauge resistance, the change in resistance of the strain gauge can be approximated as:
ΔR = R_total - R = 119.994 - 120 = -0.006 Ω
Calculation of Equivalent Strain
Substituting the calculated values in the formula, we get:
-0.006/120 = 2.0 x ε
Simplifying, we get:
ε = -0.000025 or -25 μm/m
Since the strain is negative, it means that the strain gauge experiences compression instead of tension.
Therefore, the equivalent strain is -25 μm/m or -300 μm/m (since 1 mm/m = 1000 μm/m). Hence, the correct answer is option D.
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A strain gauge of resistance 120Ω and gauge factor 2.0 is at zero strain condition A 200 kΩ fixed resistance is connected in parallel with it. Then the combination will represent an equivalent strain of (2004)a)+ 5290 m/mb)zeroc)- 123.8 m/md)- 300 m/mCorrect answer is option 'D'. Can you explain this answer?
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