A room heater is rated 400 W, 220 V. If the supply voltage drops to 200 V, what will be the power consumed (approximately)? ____.

The heater’s resistance does not change when the supply voltage changes, so we can first determine its resistance using the original rating.

$R\; =\; \backslash frac\{V^\{2\}\}\{P\}$

With the original specifications:

$V\; =\; 220\backslash \; \backslash text\{V\},\backslash qquad\; P\; =\; 400\backslash \; \backslash text\{W\}$

Substituting:

$R\; =\; \backslash frac\{220^\{2\}\}\{400\}\; =\; \backslash frac\{48\backslash ,400\}\{400\}\; =\; 121\backslash \; \backslash Omega$

Now the supply voltage drops to 200 V. The power consumed at the new voltage is

$P\text{'}\; =\; \backslash frac\{V\text{'}^\{2\}\}\{R\}$

where $V\text{'}\; =\; 200\backslash \; \backslash text\{V\}$ and $R\; =\; 121\backslash \; \backslash Omega$.

Calculate the new power:

$P\text{'}\; =\; \backslash frac\{200^\{2\}\}\{121\}\; =\; \backslash frac\{40\backslash ,000\}\{121\}\; \backslash approx\; 330.58\backslash \; \backslash text\{W\}$

Rounding to the nearest whole watt gives approximately 331 W, which matches the provided correct option.

Therefore, when the supply voltage drops to 200 V, the heater will consume about 331 W.