A wire has resistance `2Omega` at `60^@C` and a resistance of `3Omega` at `70^@C`. Temperature coefficient of resistance of wire is:

Options

A. `0.3(""^@C)^(-1)`
B. `0.03(""^@C)^(-1)`
C. `0.5(""^@C)^(-1)`
D. `0.05(""^@C)^(-1)`

Explanation

To find the temperature coefficient of resistance (α) of the wire, we can use the formula that relates the change in resistance to the change in temperature:

### Step 1: Identify the given values
- Initial resistance (R1) at temperature (T1 = 60°C): R1 = 2Ω
- Final resistance (R2) at temperature (T2 = 70°C): R2 = 3Ω

### Step 2: Calculate the change in resistance (ΔR)
\[ \Delta R = R2 - R1 = 3Ω - 2Ω = 1Ω \]

### Step 3: Calculate the change in temperature (ΔT)
\[ \Delta T = T2 - T1 = 70°C - 60°C = 10°C \]

### Step 4: Use the formula to find the temperature coefficient of resistance (α)
The formula for the temperature coefficient of resistance is given by:
\[ \alpha = \frac{\Delta R}{R1 \cdot \Delta T} \]

### Step 5: Substitute the values into the formula
\[ \alpha = \frac{1Ω}{2Ω \cdot 10°C} \]

### Step 6: Simplify the expression
\[ \alpha = \frac{1}{20} = 0.05 \, \text{per degree Celsius} \]

### Final Answer
The temperature coefficient of resistance (α) of the wire is **0.05 per degree Celsius**.

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