Question

An electric heater has been made of a nichrome coil and it runs under, $220V$, consuming $1kW$ power. It has been found that a part of its coil curried out and then it was reconnected after removing the burnt portion. Calculate the power it will consume now?

& A.\text{more than }1kW \\\ & \text{B}\text{.less than}1kW\text{,but not zero} \\\ & \text{C}.1kW \\\ & D.0kW \\\ \end{aligned}$$

Answer 1

The resistance of the material can be found by taking the ratio of the product of the resistivity and length of the wire to the area of wire. Length will be directly proportional to the resistance and the area of cross section will be inversely proportional to the resistance. This will help you in answering this question.

Complete answer:
The electrical resistance of a wire is found to be larger for a longer wire, smaller for a wire of larger cross sectional area, and would be expected to depend upon the thing out of which the wire is produced. We can express the resistance of a wire as
$R=\dfrac{\rho L}{A}$
where, $\rho$ be the resistivity which is defined as the factor in the resistance which is the quantity explaining the nature of the material. $L$ be the length of the conductor and $A$be the area of the cross section of the conductor. Using this relation, we can see that the length will be directly proportional to the resistance and the area of cross section will be inversely proportional to the resistance. In the situation mentioned in the question, the length of the nichrome coil has been reduced because of the burn and therefore the resistance will also be decreased as they are directly proportional.
If the resistance gets decreased, more current will be flowing through the coil and as a result more power will get consumed by the heater. The power consumed can be expressed by the equation given as,
$P=VI$
Therefore, the power which will get consumed now will be more than $1kW$.

Therefore the answer of the question is obtained as option A.

Note:
Resistance is defined as the measure of the opposition provided for the current flow in an electrical circuit. Resistance has been measured in ohms. Resistance is found to be dependent on the size of the object, shape, and material. This is basically the proportionality constant in the ohm’s law.