The resistance of a heating is `99Omega` at room temperature. What is the temperature of the element if the resistance is found to be `116 Omega`
(Temperature coefficient of the material of the resistor is `1.7xx10^(-4)^(2).C^(-1)`)

Options

A. `999.9^(@)C`
B. `1005.3^(@)C`
C. `1020.2^(@)C`
D. `1037.1^(@)C`

Explanation

To find the temperature of the heating element when its resistance is 116 ohms, we can use the formula that relates resistance and temperature:

\[ R_t = R_0 (1 + \alpha (T - T_0)) \]

Where:
- \( R_t \) = resistance at temperature \( T \) (116 ohms)
- \( R_0 \) = resistance at reference temperature \( T_0 \) (99 ohms)
- \( \alpha \) = temperature coefficient of resistance (1.7 x 10^(-4) °C^(-1))
- \( T_0 \) = reference temperature (room temperature, which is 27 °C)
- \( T \) = temperature we need to find

### Step 1: Write down the known values
- \( R_0 = 99 \, \Omega \)
- \( R_t = 116 \, \Omega \)
- \( \alpha = 1.7 \times 10^{-4} \, °C^{-1} \)
- \( T_0 = 27 \, °C \)

### Step 2: Substitute the known values into the formula
We substitute the known values into the resistance-temperature relationship:

\[ 116 = 99 (1 + 1.7 \times 10^{-4} (T - 27)) \]

### Step 3: Divide both sides by 99
To isolate the term with \( T \), divide both sides by 99:

\[ \frac{116}{99} = 1 + 1.7 \times 10^{-4} (T - 27) \]

Calculating \( \frac{116}{99} \):

\[ \frac{116}{99} \approx 1.1717 \]

So we have:

\[ 1.1717 = 1 + 1.7 \times 10^{-4} (T - 27) \]

### Step 4: Subtract 1 from both sides
Now, subtract 1 from both sides:

\[ 1.1717 - 1 = 1.7 \times 10^{-4} (T - 27) \]

This simplifies to:

\[ 0.1717 = 1.7 \times 10^{-4} (T - 27) \]

### Step 5: Divide both sides by \( 1.7 \times 10^{-4} \)
To solve for \( T - 27 \), divide both sides by \( 1.7 \times 10^{-4} \):

\[ T - 27 = \frac{0.1717}{1.7 \times 10^{-4}} \]

Calculating the right-hand side:

\[ T - 27 \approx 1010.59 \]

### Step 6: Add 27 to both sides
Now, add 27 to both sides to find \( T \):

\[ T \approx 1010.59 + 27 \]

Calculating this gives:

\[ T \approx 1037.59 \, °C \]

### Final Answer
The temperature of the heating element when the resistance is 116 ohms is approximately:

\[ T \approx 1037.59 \, °C \]