Step 1: Calculate resistance at a new temperature using the specified formula. \[R_t = R_0 (1 + \alpha (t - t_0))\]Where: - \( R_t \) = resistance at the new temperature - \( R_0 \) = resistance at the reference temperature - \( \alpha \) = temperature coefficient of resistance - \( t \) = new temperature - \( t_0 \) = reference temperatureProvided values: - \( R_0 = 10 \, \Omega \) - \( \alpha = 0.004 \, \text{per}^\circ \text{C} \) - \( t_0 = 20^\circ \text{C} \) - \( t = 50^\circ \text{C} \)Substitute values into the formula:\[R_t = 10 \times (1 + 0.004 \times (50 - 20)) = 10 \times (1 + 0.004 \times 30) = 10 \times (1 + 0.12) = 10 \times 1.12 = 12 \, \Omega\]Answer: The wire's resistance at \( 50^\circ \text{C} \) is \( 12 \, \Omega \). This corresponds to option (1).