Given V1 = 10 V, R1 = 100 Ω, R2 = 100 Ω, and R3 = 100 Ω, the RTD will vary from 100 Ω at 0°C to 138.5 Ω at 100°C. Ignore the resistance of the cabling. Using Fig. 23-5, solve for VAB at 20°C, where the RTD = 107.79 Ω, and at 100°C, where the RTD = 138.5 Ω.

Question

Given [latex]V_1 = 10 V, R_1 = 100 Ω, R_2 = 100 \ Ω,[/latex] and [latex]R_3 = 100[/latex] Ω, the RTD will vary from 100 Ω at 0°C to 138.5 Ω at 100°C. Ignore the resistance of the cabling. Using Fig. 23-5, solve for [latex]V_{AB}[/latex] at 20°C, where the RTD = 107.79 Ω, and at 100°C, where the RTD = 138.5 Ω.

Accepted Answer

Temperature = 20°C	Temperature = 100°C
[latex]V_{AB} = V_A − V_B[/latex]	[latex]V_{AB} = V_A − V_B[/latex]
[latex]V_{AB}=V_1\left(\frac{RTD}{R_1+RTD}\right) -V_1\left(\frac{R_3}{R_2+R_3} \right) [/latex]	[latex]V_{AB}=V_1\left(\frac{RTD}{R_1+RTD}\right) -V_1\left(\frac{R_3}{R_2+R_3} \right) [/latex]
[latex]R_2 = R_3 ∴[/latex]	[latex]R_2 = R_3 ∴[/latex]
[latex]V_{AB}=V_1\left(\frac{RTD}{R_1+RTD}\right) -V_1\left(\frac{1}{2} \right) [/latex]	[latex]V_{AB}=V_1\left(\frac{RTD}{R_1+RTD}\right) -V_1\left(\frac{1}{2} \right) [/latex]
[latex]V_{AB}=10 \ V\left(\frac{107.79 \ Ω}{100 \ Ω + 107.79 \ Ω} \right)-10 \ V \left(\frac{1}{2} \right) [/latex]	[latex]V_{AB}=10 \ V\left(\frac{138.5 \ Ω}{100 \ Ω + 138.5 \ Ω} \right)-10 \ V \left(\frac{1}{2} \right) [/latex]
[latex]V_{AB} = 187.45[/latex] mV	[latex]V_{AB} = 807.13[/latex] mV

Temperature = 20°C	Temperature = 100°C
$V_{AB} = V_A − V_B$	$V_{AB} = V_A − V_B$
$V_{AB}=V_1\left(\frac{RTD}{R_1+RTD}\right) -V_1\left(\frac{R_3}{R_2+R_3} \right)$	$V_{AB}=V_1\left(\frac{RTD}{R_1+RTD}\right) -V_1\left(\frac{R_3}{R_2+R_3} \right)$
$R_2 = R_3 ∴$	$R_2 = R_3 ∴$
$V_{AB}=V_1\left(\frac{RTD}{R_1+RTD}\right) -V_1\left(\frac{1}{2} \right)$	$V_{AB}=V_1\left(\frac{RTD}{R_1+RTD}\right) -V_1\left(\frac{1}{2} \right)$
$V_{AB}=10 \ V\left(\frac{107.79 \ Ω}{100 \ Ω + 107.79 \ Ω} \right)-10 \ V \left(\frac{1}{2} \right)$	$V_{AB}=10 \ V\left(\frac{138.5 \ Ω}{100 \ Ω + 138.5 \ Ω} \right)-10 \ V \left(\frac{1}{2} \right)$
$V_{AB} = 187.45$ mV	$V_{AB} = 807.13$ mV

Question 23.1: Given V1 = 10 V, R1 = 100 Ω, R2 = 100 Ω, and R3 = 100 Ω, the...

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