The resistance of a given electric device is 46 ohms at 25°C. If the
temperature coefficient of resistance of the material is 0.004545 at 20°C. Solve for the temperature of the device when its resistance is 92 ohms?�
asdasd
Why did the electric device go on a diet? Because it wanted to decrease its resistance!
But to solve your question, we can use the formula for temperature change and resistance change in terms of temperature coefficient:
ΔR = R₀ * α * ΔT
Where:
ΔR is the change in resistance
R₀ is the initial resistance at 25°C
α is the temperature coefficient of resistance
ΔT is the change in temperature
We know that ΔR = 92 ohms - 46 ohms = 46 ohms, R₀ = 46 ohms, and α = 0.004545.
Let's rearrange the formula to solve for ΔT:
ΔT = ΔR / (R₀ * α)
Substituting the values:
ΔT = 46 ohms / (46 ohms * 0.004545)
Calculating ΔT:
ΔT ≈ 20°C
Adding this temperature change to the initial temperature of 25°C, we can find the temperature of the device:
Temperature = 25°C + ΔT ≈ 25°C + 20°C
Temperature ≈ 45°C
So, the temperature of the device when its resistance is 92 ohms is approximately 45°C. Just keep in mind, my calculations are jokingly precise!
To solve for the temperature of the device when its resistance is 92 ohms, we can use the formula for the temperature coefficient of resistance (α):
α = (R2 - R1) / (R1 * ΔT)
Where:
α = temperature coefficient of resistance
R1 = initial resistance of the device at a known temperature (25°C)
R2 = final resistance of the device (92 ohms)
ΔT = change in temperature (T2 - T1)
Since the temperature coefficient is given at 20°C, we can use this as T1. Let's solve for ΔT:
α = (R2 - R1) / (R1 * ΔT)
0.004545 = (92 - 46) / (46 * ΔT)
0.004545 = 46 / (46 * ΔT)
Divide both sides of the equation by 46:
0.004545 / 46 = 1 / ΔT
0.000098913 = 1 / ΔT
ΔT = 1 / 0.000098913
ΔT ≈ 10,109.68°C
Now, we can find the final temperature (T2) by subtracting ΔT from the initial temperature (T1):
T2 = T1 - ΔT
T2 = 20°C - 10,109.68°C
T2 ≈ -10,089.68°C
Therefore, the temperature of the device when its resistance is 92 ohms is approximately -10,089.68°C.
To solve for the temperature of the device when its resistance is 92 ohms, we can use the temperature coefficient of resistance.
The temperature coefficient of resistance is defined as the change in resistance per degree Celsius change in temperature. In this case, the temperature coefficient of resistance is given as 0.004545 ohms/°C at 20°C.
First, let's find the change in resistance.
Change in resistance = new resistance - initial resistance
= 92 ohms - 46 ohms
= 46 ohms
Next, let's find the change in temperature.
Change in temperature = change in resistance / temperature coefficient of resistance
= 46 ohms / 0.004545 ohms/°C
≈ 10119.5 °C
Finally, let's find the temperature of the device.
Temperature of the device = initial temperature + change in temperature
= 25°C + 10119.5 °C
≈ 10144.5 °C
Therefore, the temperature of the device when its resistance is 92 ohms is approximately 10144.5 °C.