Two different conductors have same resistance at `0^@` C It is found that the resistance of the first conductor at `t_1^@` C is equal to the resistance of the second conductor at `t_2^@` C. The ratio of temperature coefficients of resistance of the conductors,`a_1/a_2` is

Options

A. `t_1/t_2`
B. `(t_2-t_1)/t_2`
C. `(t_2-t_1)/t_1`
D. `t_2/t_1`

Answer

To solve the problem, we need to establish the relationship between the resistances of the two conductors at different temperatures and derive the ratio of their temperature coefficients of resistance.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- Let the resistance of both conductors at \(0^\circ C\) be \(R\).
- The temperature coefficients of resistance for the first and second conductors are denoted as \(\alpha_1\) and \(\alpha_2\) respectively.

2. **Resistance at Different Temperatures**:
- The resistance of the first conductor at \(t_1^\circ C\) can be expressed as:
\[ R_1 = R(1 + \alpha_1 t_1) \]
- The resistance of the second conductor at \(t_2^\circ C\) can be expressed as:
\[ R_2 = R(1 + \alpha_2 t_2) \]

3. **Setting Up the Equation**:
- According to the problem, the resistance of the first conductor at \(t_1^\circ C\) is equal to the resistance of the second conductor at \(t_2^\circ C\):
\[ R(1 + \alpha_1 t_1) = R(1 + \alpha_2 t_2) \]

4. **Cancelling the Resistance**:
- Since \(R\) is the same for both conductors and is not zero, we can divide both sides by \(R\):
\[ 1 + \alpha_1 t_1 = 1 + \alpha_2 t_2 \]

5. **Simplifying the Equation**:
- By subtracting 1 from both sides, we get:
\[ \alpha_1 t_1 = \alpha_2 t_2 \]

6. **Finding the Ratio of Temperature Coefficients**:
- Rearranging the equation gives us:
\[ \frac{\alpha_1}{\alpha_2} = \frac{t_2}{t_1} \]

### Final Result:
Thus, the ratio of the temperature coefficients of resistance of the two conductors is:
\[ \frac{\alpha_1}{\alpha_2} = \frac{t_2}{t_1} \]