If the cold junction of thermocouple is kept at `0^(@)C` and the hot junction is kept at `T^(@)C`, then the relation between neutral temperature `(T_(n))` and temperature of inversion `(T_(i))` is

Options

A. `T_(n) =(T_(i))/2`
B. `T_(n)=2T_(i)`
C. `T_(n) =T_(i)-T`
D. `T_(n)=T_(i)+T`

Answer

To solve the problem, we need to establish the relationship between the neutral temperature \( T_n \) and the temperature of inversion \( T_i \) in a thermocouple setup where the cold junction is at \( 0^\circ C \) and the hot junction is at \( T^\circ C \).

### Step-by-Step Solution:

1. **Understanding the Terms**:
- The cold junction temperature \( T_c \) is given as \( 0^\circ C \).
- The hot junction temperature is \( T \) (which is \( T^\circ C \)).
- The neutral temperature is denoted as \( T_n \).
- The temperature of inversion is denoted as \( T_i \).

2. **Establishing the Relationship**:
- For a thermocouple, the relationship between the inversion temperature \( T_i \), neutral temperature \( T_n \), and cold junction temperature \( T_c \) can be expressed as:
\[ T_i - T_n = T_n - T_c \]

3. **Substituting the Cold Junction Temperature**:
- Since \( T_c = 0^\circ C \), we can substitute this into the equation:
\[ T_i - T_n = T_n - 0 \]
- This simplifies to:
\[ T_i - T_n = T_n \]

4. **Rearranging the Equation**:
- Rearranging the equation gives:
\[ T_i = 2T_n \]

5. **Expressing Neutral Temperature in Terms of Inversion Temperature**:
- From the equation \( T_i = 2T_n \), we can express \( T_n \) in terms of \( T_i \):
\[ T_n = \frac{T_i}{2} \]

6. **Conclusion**:
- The relationship between the neutral temperature \( T_n \) and the temperature of inversion \( T_i \) is:
\[ T_n = \frac{T_i}{2} \]

### Final Answer:
The correct relation is \( T_n = \frac{T_i}{2} \).