Question

A heating element has a resistance of 100\[\Omega \] at room temperature. When it is connected to a supply of 220 V, a steady current of 2A passes in it and temperature is 500℃ more than room temperature. What is the temperature coefficient of resistance of the heating element?
A 1×10$^{ - 4}$℃$^{ - 1}$
B 5×10$^{ - 4}$℃$^{ - 1}$
C 2×10$^{ - 4}$℃$^{ - 1}$
D 0.5×10$^{ - 4}$℃$^{ - 1}$

Answer 1

Hint:
 According to ohm's law V=IR.
Therefore resistance can be written as R=V/I. Due to heating the new resistance of the heating element can be written as R=$R_0$(1+$\alpha$T). Where $R_0$ is the initial resistance, $\alpha$ is temperature coefficient and T is change in temperature. Now upon equating both the resistance we get the coefficient of resistance, i.e. $\dfrac{V}{I}$ = $R_0$ (1+αT).

Complete step by step answer:
Given, the initial resistance of the heating element, RO=100
voltage, V=220
current, I=2
increase in temperature, T=500.
According to ohm's law V=IR.
Therefore, R=V/I
Substituting the value of voltage and current we get
R=$\dfrac{{220}}{2}$=110$\Omega $
Now due to heating the new resistance, R of the heating element can be written as R =$R_0$(1+ αT).
R=100(1+$\alpha$ 500)
Upon equating both the equations we get,
110=100(1+$\alpha$ 500)
$\implies (1+\alpha50) = \dfrac{{11}}{{10}} = 1.1$
$\implies 500 \alpha = 1.1-1$
$\therefore$ $\alpha$ = 2×10$^{ - 4}$℃$^{ - 1}$
Therefore the temperature coefficient of resistance of the heating element is 2×10$^{ - 4}$℃$^{ - 1}$.

So, the correct answer is “Option C”.

Additional Information:
Ohm's Law is a formula used to calculate the relationship between voltage, current and resistance in an electrical circuit, V=IR.

Note:
All the quantity should be written in the SI unit. Some simple laws of physics should be known to solve such types of questions. Here ohm's law is applied.