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 that 1 kW, but not zero
• C. 1 kW
• D. OkW

Answer 1

Answer: (A)

The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend upon the material out of which the wire is made.The resistance of a wire can be expressed as $R=\rho \frac{L}{A}$,
where,
$\rho$ - Resistivity - the factor in the resistance which takes into account the nature of the material is the resistivity
L - Length of the conductor
A - Area of cross section of the conductor.
From this relation, we observe that the length is directly proportional to the resistance and the area of cross section is inversely proportional to the resistance.
In this case, the length of the nichrome coil is reduced due to the burn and so the resistance will also be reduced proportionally.
When the resistance is decreased, more current flows through the coil and apparently, more power is consumed by the heater as power consumed P = VI.
Hence, the power it will consume now is more than 1 kW.