a) A thermocouple circuit uses a Chromel-Alumel thermocouple which gives an e.m.f. of 35.4*mV* when measuring a temperature of , with reference temperature . The resistance of the meter coil  is  and a current of 0.1*mA* gives full scale deflection. The resistance of junction and leads, Calculate:

i. Resistance of the series resistance if a temperature of is to give full scale deflection.      **[2 Marks]**

The approximate error due to rise of

To solve the problem, let's break it down step by step. The goal is to calculate the series resistance required to achieve full-scale deflection on a meter, using the given thermocouple and circuit parameters.

### Given Data:

- **Thermocouple e.m.f. (\( V_{\text{emf}} \))**: 35.4 mV
- **Full-scale deflection current (\( I_{\text{fsd}} \))**: 0.1 mA = 0.1 × 10⁻³ A
- **Resistance of the meter coil (\( R_{\text{meter}} \))**: 10 Ω
- **Resistance of the junction and leads (\( R_{\text{j+l}} \))**: 2 Ω

### i. Calculate the Series Resistance \( R_s \)

To find the series resistance \( R_s \), we use Ohm's law. For full-scale deflection:

\[
V_{\text{total}} = I_{\text{fsd}} \times (R_s + R_{\text{meter}} + R_{\text{j+l}})
\]

Where:

\[
V_{\text{total}} = V_{\text{emf}} = 35.4 \, \text{mV} = 35.4 \times 10^{-3} \, \text{V}
\]

\[
I_{\text{fsd}} = 0.1 \times 10^{-3} \, \text{A}
\]

\[
R_{\text{total}} = R_s + R_{\text{meter}} + R_{\text{j+l}} = R_s + 10 \, \Omega + 2 \, \Omega
\]

Thus:

\[
35.4 \times 10^{-3} = 0.1 \times 10^{-3} \times (R_s + 12)
\]

Now, solve for \( R_s \):

\[
35.4 \times 10^{-3} = 0.1 \times 10^{-3} R_s + 0.1 \times 10^{-3} \times 12
\]

\[
35.4 \times 10^{-3} = 0.1 \times 10^{-3} R_s + 1.2 \times 10^{-3}
\]

\[
35.4 \times 10^{-3} - 1.2 \times 10^{-3} = 0.1 \times 10^{-3} R_s
\]

\[
34.2 \times 10^{-3} = 0.1 \times 10^{-3} R_s
\]

\[
R_s = \frac{34.2 \times 10^{-3}}{0.1 \times 10^{-3}} = 342 \, \Omega
\]

**The required series resistance \( R_s \) is 342 Ω.**

### Approximate Error Due to a Rise in Temperature

The problem seems to be incomplete regarding the "approximate error due to rise of..." We would need more information on the specific rise in temperature, how the thermocouple voltage changes with temperature, or how the resistance changes due to temperature to calculate the error.

Would you like more details or clarification? Here are some additional questions to consider:

1. How does the thermocouple voltage vary with temperature?
2. What assumptions are we making regarding the linearity of the thermocouple response?
3. How would changes in resistance due to temperature affect the circuit?
4. Can we calculate the error if we know the temperature coefficient of resistance?
5. How does the reference junction temperature influence the thermocouple's output?

**Tip:** When working with thermocouples, it's essential to consider the temperature dependence of the materials used, as this can significantly affect the accuracy of your measurements.

Learn how to calculate the series resistance required for full-scale deflection in a thermocouple circuit. This problem involves using Ohm's Law and understanding the behavior of thermocouples. Suitable for undergraduate students studying electrical circuits.

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