Question

An electric heater consists of a nichrome coil and runs under 220 V, consuming $1\,kw$ power. Part of its coil burned out and it was reconnected after cutting off the burnt portion. The power it will consume now is
A. more than $1\,kw$
B. Less than$1\,kw$, but not zero
C. $1\,kw$
D. $0\,kw$

Answer 1

The resistance of a wire is directly proportional to the length of the wire and Power is directly proportional to the current flowing through a conductor. Use the relation for the resistance of a wire in terms of length, area and resistivity. Then use the formula of power to find the power consumed.

Complete step by step answer:
The resistance of wire is given by the relation, $R = \rho \dfrac{l}{A}$, where l is the length of the wire, A is the area of cross section of the wire and $\rho$ is the resistivity of the material of the wire. From this relation we see that the resistance of a wire is directly proportional to the length of the wire and inversely proportional to the area of the cross-section. It also depends upon the nature of the material of the wire.
In the given situation part of the nichrome coil burned out and it was reconnected after cutting off the burnt portion. Therefore its length gets reduced and hence the resistance will get reduced proportionally.
As the current flowing through a conductor is given by the Ohm’s law i.e. V = IR.
So, if the resistance of a wire gets decreased, more current will flow through it.
Also, power consumed is given by the relation P = VI. From this relation we can see that the power consumed by a conductor is directly proportional to the current flowing through it. So, if more current starts flowing through a conductor more power will it consume.
So, in the given case power consumed will be more than $1\,kw$.

So, the correct answer is “Option C”.

Note:
It should be noted that if potential difference across the conductor is changed the resistance of the wire will change. Also, if the area of the cross section changes then the resistance of a wire also changes. Also we have

\Rightarrow \dfrac{P}{{{I^2}}} = \rho \dfrac{l}{A} \Rightarrow P = {I^2}\rho \dfrac{l}{A}$$. Hence if current flowing through a conductor remains the same, power consumed is directly proportional to the length of the wire.