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A heating element has a resistance of 100 Ω at room temperature. When it is connected to a supply of 220 V, a steady current of 2 A passes in it and temperature is 500°C more than room temperature. What is the temperature coefficient of resistance of the heating element?
- a)5 × 10-4 °C-1
- b)2 × 10-4 °C-1
- c)1 × 10-4 °C-1
- d)0.5 × 10-4 °C-1
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A heating element has a resistance of 100Ωat room temperature. W...
Understanding the Problem
To determine the temperature coefficient of resistance (α) of the heating element, we start with the given values:
- Initial resistance (R0) = 100 Ω at room temperature
- Voltage (V) = 220 V
- Current (I) = 2 A
- Temperature increase (ΔT) = 500 °C
Calculating the Resistance at 500 °C
Using Ohm's Law, we can find the resistance when the current is steady:
- R = V / I = 220 V / 2 A = 110 Ω
Now, this resistance (R) represents the resistance at room temperature plus the additional resistance due to the temperature increase.
Finding the Change in Resistance
The change in resistance (ΔR) can be calculated as:
- ΔR = R - R0 = 110 Ω - 100 Ω = 10 Ω
Using the Temperature Coefficient Formula
The formula for the change in resistance based on temperature coefficient is given by:
- ΔR = R0 * α * ΔT
Rearranging this to find α gives us:
- α = ΔR / (R0 * ΔT)
Substituting the values:
- α = 10 Ω / (100 Ω * 500 °C) = 10 / 50000 = 0.0002 °C^-1
Final Answer
Thus, the temperature coefficient of resistance is:
- α = 2 × 10^-4 °C^-1
Therefore, the correct answer is option 'B'.
To determine the temperature coefficient of resistance (α) of the heating element, we start with the given values:
- Initial resistance (R0) = 100 Ω at room temperature
- Voltage (V) = 220 V
- Current (I) = 2 A
- Temperature increase (ΔT) = 500 °C
Calculating the Resistance at 500 °C
Using Ohm's Law, we can find the resistance when the current is steady:
- R = V / I = 220 V / 2 A = 110 Ω
Now, this resistance (R) represents the resistance at room temperature plus the additional resistance due to the temperature increase.
Finding the Change in Resistance
The change in resistance (ΔR) can be calculated as:
- ΔR = R - R0 = 110 Ω - 100 Ω = 10 Ω
Using the Temperature Coefficient Formula
The formula for the change in resistance based on temperature coefficient is given by:
- ΔR = R0 * α * ΔT
Rearranging this to find α gives us:
- α = ΔR / (R0 * ΔT)
Substituting the values:
- α = 10 Ω / (100 Ω * 500 °C) = 10 / 50000 = 0.0002 °C^-1
Final Answer
Thus, the temperature coefficient of resistance is:
- α = 2 × 10^-4 °C^-1
Therefore, the correct answer is option 'B'.
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Community Answer
A heating element has a resistance of 100Ωat room temperature. W...
Resistance after temperature increases by 500°C = 220/2 = 110 Ω
The variation of the resistance with temperature is given by:
R2 = R1(1 +21
110 = 100(1 +)
The variation of the resistance with temperature is given by:
R2 = R1(1 +
α(T
- T
))
110 = 100(1 +
α × 500
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A heating element has a resistance of 100Ωat room temperature. When it is connected to a supply of 220 V, a steady current of 2 A passes in it and temperature is 500°C more than room temperature. What is the temperature coefficient of resistance of the heating element?a)5 × 10-4°C-1b)2 × 10-4°C-1c)1 × 10-4°C-1d)0.5 × 10-4°C-1Correct answer is option 'B'. Can you explain this answer?
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