Question

Сопротивление вольфрановой нити лампы при 20 градусов С равно 20 Ом. сопротивление той же нити в рабочем состоянии 188 Ом. какова температура накала нити?

Answer 1

R₂=R₁*(1+α*(t₂-t₁))

α=0.0041 1/K - температурный коэф. вольфрама при 20°С

188=20*(1+0,0041*(х-293))

188=0,082х-4,026

х=2342° К  =2069° С

Answer 2

Calculating the Temperature of the Tungsten Filament

To calculate the temperature of the tungsten filament, we can use the formula for the resistance of the filament at different temperatures. The resistance of the filament at room temperature (20°C) is given as 20 ohms, and in the working state, it is 188 ohms.

Using the formula for resistance-temperature relationship: \[ R = R_0 \times (1 + \alpha \times (T - T_0)) \]

Where: - \( R \) = resistance at temperature \( T \) - \( R_0 \) = resistance at reference temperature \( T_0 \) (20°C in this case) - \( \alpha \) = temperature coefficient of resistance for tungsten (approximately 0.0045/°C)

Calculation

Using the given resistances: - \( R_0 = 20 \, \Omega \) - \( R = 188 \, \Omega \) - \( T_0 = 20°C \) - \( \alpha = 0.0045/°C \)

We can rearrange the formula to solve for the temperature \( T \): \[ T = \frac{R - R_0}{R_0 \times \alpha} + T_0 \]

Substituting the given values: \[ T = \frac{188 - 20}{20 \times 0.0045} + 20 \]

\[ T \approx 2300°C \]

The approximate temperature of the tungsten filament in the working state is 2300°C.