Question

An electric heater consists of a nichrome coil and runs under 220V, consuming 1kW 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 1kW
B) Less than 1kW, but not zero.
C) 1kW
D) 0kW

Answer 1

Hint: An electric heater is given which has 220V voltage and 1kW power, it will also have some current flowing through it and resistance which will oppose it. The resistance is dependent on the length, so when portion burnt is removed and the coil is reconnected there will be change in length and so resistance. Hence by taking account all the changes in the given parameter we can find the change in power.

Formula used:
\[\begin{align}
  & P=VI \\
 & R=\rho \dfrac{l}{A} \\
\end{align}\]

Complete step-by-step answer:
Resistance of a material is its ability to oppose the current flowing through it. Resistance of a coil can be given as
\[R=\rho \dfrac{l}{A}\]
Where L is the length of the wire used in the coil, A is the cross sectional area and ρ is the resistivity.

From the above formula we can see that the resistance is directly proportional to the length of the wire. Smaller the length, smaller the resistance.
Here in the question when the burnt part of the coil was removed and then reconnected which implies the length is reduced. Hence the resistance will also reduce.
Now the power is given as product of voltage and current, that is
\[P=VI\]
As resistance is reduced more current will be flowing through the coil, and from the above equation we can see that power is directly proportional to current. Hence with increase in current there will be increase in power. Here voltage remains constant as when resistance increases, current decreases which will balance the change for voltage and voltage remains constant.

So, the correct answer is “Option A”.

Note: In case current remains constant after removing the burnt part, then power will be directly proportional to resistance and it will reduce. As current is constant and resistance will change the voltage will change as per resistance. Because voltage is given as a product of current and resistance. Hence voltage will reduce and current, so does power.