A thermocouple circuit uses Chrome - Alumel which gives an e.m.f of 33.3 mV when
measuring a temperature of 800 oC with reference temperature of 0 oC. The resistance of
the metal coil is Rm = 50 Ω and current of 0.1 mA gives a full scale deflection. The
resistance of the junction and leads Re = 12 Ω. Determine,
i. Resistance of the series resistance if a temperature of 800 oC is to give full scale
deflection
ii. The approximate error due to rise of 1Ω in Re
iii. The approximate error due to rise of 10 oC in a copper coil of the meter. The
resistance temperature coefficient of the coil is 0.00426 /oC [10]
Answers
Answer:
A thermocouple circuit uses a chromel- alumel thermocouple which gives an emf of 33.3 v ... of 800oc with reference temperature 0oc. the resistance of the meter coil,
Given :
emf = 33.3mV
Rm = 50Ω
I = 0.1mA
Re = 12Ω
∝ = 0.00426 /°C
To find :
i) Resistance of the series resistance if a temperature of 800°C is to give full scale deflection
ii) The approximate error due to rise of 1Ω in Re
iii) The approximate error due to rise of 10°C in a copper coil of the meter.
Solution :
i) Let series resistance be Rs
emf = I (Rm + Rs + Re)
Rs = (emf / I) - Rm - Re
Rs = (33.3 × 10⁻³) / (0.1 × 10⁻³) - 50 - 12
Rs = 333 - 62
Rs = 271Ω
ii) Due to rise of 1Ω in Re
Now new Re is Re' = 1 + 12 = 13Ω
emf = I' (Rm + Re' + Rs)
I' = emf / (Rm + Re' + Rs)
I' = (33.3 × 10⁻³) / (50 + 271 + 13)
I' = 0.0997mA
Approximate error in temperature = [(I' - I) / I] × 100
= [(0.0997 - 0.1) / 0.1] × 800
= - 0.3%
iii) Change in resistance with a temperature increase of 10°C
ΔRm = Rm × ∝ × 10°C
= 50 × 0.00426 × 10
= 2.13Ω
New Rm' = Rm + ΔRm
Rm' = 50 + 2.13
Rm' = 52.13Ω
Now current I'' = emf / (Rm' + Rs +Re)
I'' = 0.09936mA
Therefore approximate error in temperature = ([I'' - I) / I] × 100
= -0.64%