A cell of emf 1.6 V is connected across a potentiometer wire of length 500 cm. The cell has negligible resistance. A thermo couple whose cold junction is at `0^@ `C and hot junction at `80^@ C` is connected in the secondary circuit. The balancing length is found to be 125 cm. Find the thermo emf per degree centigrade difference of temperature of the junctions.

Options

A. `0.005 V//^@ C`
B. `0.05 V//^@ C `
C. `0.5 V//^@C `
D. `5V//^@ C`

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the given data
- EMF of the cell (E) = 1.6 V
- Length of the potentiometer wire (L_total) = 500 cm
- Balancing length (L_balancing) = 125 cm
- Temperature of cold junction (T_cold) = 0 °C
- Temperature of hot junction (T_hot) = 80 °C

### Step 2: Calculate the thermo EMF (E_th) using the formula
The thermo EMF can be calculated using the formula:
\[ E_{th} = \frac{L_{balancing}}{L_{total}} \times E \]
Where:
- \(E_{th}\) is the thermo EMF,
- \(L_{balancing}\) is the balancing length,
- \(L_{total}\) is the total length of the potentiometer wire,
- \(E\) is the EMF of the cell.

### Step 3: Substitute the values into the formula
Substituting the known values:
\[ E_{th} = \frac{125 \, \text{cm}}{500 \, \text{cm}} \times 1.6 \, \text{V} \]

### Step 4: Simplify the expression
Calculating the fraction:
\[ E_{th} = \frac{125}{500} \times 1.6 = 0.25 \times 1.6 = 0.4 \, \text{V} \]

### Step 5: Convert the thermo EMF to mV
Since we want the answer in volts:
\[ E_{th} = 0.4 \, \text{V} = 40 \times 10^{-2} \, \text{V} \]

### Step 6: Calculate the temperature difference
The temperature difference between the hot and cold junctions is:
\[ \Delta T = T_{hot} - T_{cold} = 80 \, \text{°C} - 0 \, \text{°C} = 80 \, \text{°C} \]

### Step 7: Find the thermo EMF per degree Celsius
To find the thermo EMF per degree Celsius, we divide the thermo EMF by the temperature difference:
\[ E_{per \, degree} = \frac{E_{th}}{\Delta T} = \frac{40 \times 10^{-2} \, \text{V}}{80 \, \text{°C}} \]

### Step 8: Calculate the final value
Calculating the final value:
\[ E_{per \, degree} = \frac{0.4 \, \text{V}}{80} = 0.005 \, \text{V/°C} \]

### Final Answer
The thermo EMF per degree centigrade difference of temperature of the junctions is:
\[ \boxed{0.005 \, \text{V/°C}} \]