An electrical resistance strain gauge of resistance 120Ω has a gauge factor of 2. It is bonded to a steel specimen (modulus of elasticity, E = 2 * 1011 N/m2) for measuring strain. Estimate: (2002)(a) Strain induced in the specimen if tensile stress of 60 * 106 N/m2 is applied on the specimen.(b) Change in the electrical resistance of the gauge due to the tensile stress as given in (a)(c) Change in the electrical resistance of the gauge if there is an increase of temperature by 40°C.Assume the following data:Temperature coefficient of resistance of gauge is 20 * 10-6 per °CThermal coefficient of linear expansion of the gauge is 16 * 10-6 per °C.Thermal coefficient of linear expansion of steel specimen is 12 * 10-6 per °C.Correct answer is '0.3'. Can you explain this answer?

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An electrical resistance strain gauge of resistance 120Ω has a gauge factor of 2. It is bonded to a steel specimen (modulus of elasticity, E = 2 * 10¹¹ N/m²) for measuring strain. Estimate: (2002)

(a) Strain induced in the specimen if tensile stress of 60 * 10⁶ N/m² is applied on the specimen.

(b) Change in the electrical resistance of the gauge due to the tensile stress as given in (a)

Assume the following data:

Temperature coefficient of resistance of gauge is 20 * 10^-6 per °C

Thermal coefficient of linear expansion of the gauge is 16 * 10^-6 per °C.

Thermal coefficient of linear expansion of steel specimen is 12 * 10^-6 per °C.

Correct answer is '0.3'. Can you explain this answer?

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An electrical resistance strain gauge of resistance 120Ω has a gauge ...

Given R = Resistance = 120Ω

G_f= Gauge factor = 2

E = 2 x 10¹¹ N/m²

(a) Tensile stress = 60 x 10⁶ N/m²

We know that,

where ΔR = change in resistance

∴ ΔR = G_f x ε x R

= 2 x 0.3 x 10^-3 x 120

= 0.072Ω

AR1 = change in resistance due to temperature increase

= R (1 + α_g ΔT) = 120 (1 + 20 x 10⁶ x 40) = 120.096Ω

where α_g = temperature coefficient of resistance of gauge.

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Most Upvoted Answer

An electrical resistance strain gauge of resistance 120Ω has a gauge ...

Given:

Resistance of strain gauge, R = 120Ω

Gauge factor, GF = 2

Modulus of elasticity of steel specimen, E = 2 * 10^11 N/m^2

Stress applied, σ = 60 * 10^6 N/m^2

Temperature coefficient of resistance of gauge, αg = 20 * 10^-6 per °C

Thermal coefficient of linear expansion of gauge, βg = 16 * 10^-6 per °C

Thermal coefficient of linear expansion of steel specimen, βs = 12 * 10^-6 per °C

Change in temperature, ΔT = 40°C

(a) Strain induced in the specimen:

Strain induced, ε = σ/E = (60 * 10^6 N/m^2)/(2 * 10^11 N/m^2) = 0.0003

(b) Change in the electrical resistance:

Change in resistance of the gauge, ΔR = GF * R * ε = 2 * 120Ω * 0.0003 = 0.072Ω

(c) Change in the electrical resistance due to temperature:

Change in resistance of the gauge due to temperature, ΔRt = R * αg * ΔT = 120Ω * 20 * 10^-6 per °C * 40°C = 0.096Ω

Change in resistance of the gauge due to thermal expansion, ΔRe = R * βg * ΔT = 120Ω * 16 * 10^-6 per °C * 40°C = 0.0768Ω

Change in resistance of steel specimen due to thermal expansion, ΔRs = R * βs * ΔT * ε = 120Ω * 12 * 10^-6 per °C * 40°C * 0.0003 = 0.0144Ω

Total change in resistance, ΔRtotal = ΔRt + ΔRe + ΔRs = 0.096Ω + 0.0768Ω + 0.0144Ω = 0.1872Ω

Final answer:

Change in resistance of the gauge due to tensile stress, ΔR = 0.072Ω

Change in resistance of the gauge due to temperature, ΔRtotal = 0.1872Ω

Total change in resistance, ΔRtotal = ΔR + ΔRtotal = 0.072Ω + 0.1872Ω = 0.2592Ω

Final strain induced in the specimen, ε = ΔRtotal/(GF * R) = 0.2592Ω/(2 * 120Ω) = 0.00136

Therefore, the final answer is 0.0014 (approximated to 3 significant figures).

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An electrical resistance strain gauge of resistance 120Ω has a gauge factor of 2. It is bonded to a steel specimen (modulus of elasticity, E = 2 * 1011 N/m2) for measuring strain. Estimate: (2002)(a) Strain induced in the specimen if tensile stress of 60 * 106 N/m2 is applied on the specimen.(b) Change in the electrical resistance of the gauge due to the tensile stress as given in (a)(c) Change in the electrical resistance of the gauge if there is an increase of temperature by 40°C.Assume the following data:Temperature coefficient of resistance of gauge is 20 * 10-6 per °CThermal coefficient of linear expansion of the gauge is 16 * 10-6 per °C.Thermal coefficient of linear expansion of steel specimen is 12 * 10-6 per °C.Correct answer is '0.3'. Can you explain this answer?

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An electrical resistance strain gauge of resistance 120Ω has a gauge factor of 2. It is bonded to a steel specimen (modulus of elasticity, E = 2 * 1011 N/m2) for measuring strain. Estimate: (2002)(a) Strain induced in the specimen if tensile stress of 60 * 106 N/m2 is applied on the specimen.(b) Change in the electrical resistance of the gauge due to the tensile stress as given in (a)(c) Change in the electrical resistance of the gauge if there is an increase of temperature by 40°C.Assume the following data:Temperature coefficient of resistance of gauge is 20 * 10-6 per °CThermal coefficient of linear expansion of the gauge is 16 * 10-6 per °C.Thermal coefficient of linear expansion of steel specimen is 12 * 10-6 per °C.Correct answer is '0.3'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about An electrical resistance strain gauge of resistance 120Ω has a gauge factor of 2. It is bonded to a steel specimen (modulus of elasticity, E = 2 * 1011 N/m2) for measuring strain. Estimate: (2002)(a) Strain induced in the specimen if tensile stress of 60 * 106 N/m2 is applied on the specimen.(b) Change in the electrical resistance of the gauge due to the tensile stress as given in (a)(c) Change in the electrical resistance of the gauge if there is an increase of temperature by 40°C.Assume the following data:Temperature coefficient of resistance of gauge is 20 * 10-6 per °CThermal coefficient of linear expansion of the gauge is 16 * 10-6 per °C.Thermal coefficient of linear expansion of steel specimen is 12 * 10-6 per °C.Correct answer is '0.3'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electrical resistance strain gauge of resistance 120Ω has a gauge factor of 2. It is bonded to a steel specimen (modulus of elasticity, E = 2 * 1011 N/m2) for measuring strain. Estimate: (2002)(a) Strain induced in the specimen if tensile stress of 60 * 106 N/m2 is applied on the specimen.(b) Change in the electrical resistance of the gauge due to the tensile stress as given in (a)(c) Change in the electrical resistance of the gauge if there is an increase of temperature by 40°C.Assume the following data:Temperature coefficient of resistance of gauge is 20 * 10-6 per °CThermal coefficient of linear expansion of the gauge is 16 * 10-6 per °C.Thermal coefficient of linear expansion of steel specimen is 12 * 10-6 per °C.Correct answer is '0.3'. Can you explain this answer?.

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