What will be the value of current and resistance in each case if an electric heater
consumes energy at a rate of 1000 W when heating is at the maximum rate and 500 W
when the heating is at the minimum and the voltage is 220 V?

Solution,
Resistance is a material property that doesn't change with applied potential difference or the amount of current flowing through it.
Current across the heater may vary depending on the potential difference applied across it.
Given,
For a given heater with the same coil, the current cannot be varied without varying the potential difference across it.
Since, it is given that the voltage is fixed at 220 V, it means that the heater coil is different in case of 1000 W and 500 W.

For 1000 W electric heater,
the resistance (R₁) of the heater coil will be given by the relation:
$$\begin{gathered} P=\frac{V^2}{R_1} \\ {R}_1=\frac{V^2}{P}=\frac{220\times 220}{1000}=48.4 ohm \end{gathered}$$
Let the current through the heater be I₁.
Then, using the relation,
$$\begin{gathered} P={I_1}^2{R}_1 \\ {I}_1=\sqrt{\frac{P}{R_1}}=\sqrt{\frac{1000}{48.4}}=4.545 A = 4.55A \end{gathered}$$

For 500 W electric heater,
the resistance (R₂) of the heater coil will be given by the relation:
$$\begin{gathered} P=\frac{V^2}{R_2} \\ {R}_2=\frac{V^2}{P}=\frac{220\times 220}{500}=96.8 ohm \end{gathered}$$
Let the current through the heater be I2.
Then, using the relation,
$$\begin{gathered} P={I_2}^2{R}_2 \\ {I}_2=\sqrt{\frac{P}{R_2}}=\sqrt{\frac{500}{96.8}}=2.27A \end{gathered}$$

So, comparing a 1000 W electric heater and a 500 W electric heater, the resistance of a 500 W electric heater will be double that of a 1000 W electric heater and the current drawn by a 500 W electric heater will be half that of the 1000 W electric heater (when operated at a potential difference of 220 V).