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 the room temperature. The temperature coefficient of resistance of the heating element is

Question

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 the room temperature. The temperature coefficient of resistance of the heating element is (A) 5 × 10-4 o C -1 (B) 2 × 10-4 o C -1 (C) 1 × 10-4 o C -1 (D) 0.5 × 10-4 o C -1

Tardigrade Admin · Accepted Answer

Resistance of heating element after temperature increases by

50 0^{o} C = \frac{220}{2} = 110 Ω

(from Ohm's law). The new resistance is related to the temperature coefficient of the heating element as

110 = 100 (1 + α 500)

α = \frac{10}{100 \times 500} \Rightarrow α = 2 \times 1 0^{- 4}^{\circ} C^{- 1}

Q. 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 $500^{\circ} C$ more than the room temperature. The temperature coefficient of resistance of the heating element is

$5 \times 1 0^{- 4}^{o} C^{- 1}$

$2 \times 1 0^{- 4}^{o} C^{- 1}$

$1 \times 1 0^{- 4}^{o} C^{- 1}$

$0.5 \times 1 0^{- 4}^{o} C^{- 1}$

Q. A heating element has a resistance of 100Ω at room temperature. When it is connected to a supply of 220V , a steady current of 2A passes in it and temperature is 500∘C more than the room temperature. The temperature coefficient of resistance of the heating element is

5×10−4oC−1

2×10−4oC−1

1×10−4oC−1

0.5×10−4oC−1

Resistance of heating element after temperature increases by 500oC=2220​=110Ω (from Ohm's law). The new resistance is related to the temperature coefficient of the heating element as 110=100(1+α500) α=100×50010​⇒α=2×10−4∘C−1

Q. 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 $500^{\circ} C$ more than the room temperature. The temperature coefficient of resistance of the heating element is

$5 \times 1 0^{- 4}^{o} C^{- 1}$

$2 \times 1 0^{- 4}^{o} C^{- 1}$

$1 \times 1 0^{- 4}^{o} C^{- 1}$

$0.5 \times 1 0^{- 4}^{o} C^{- 1}$