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The diagram above shows a $ {400\space \Omega }$ resistor connected in series to a variable resistor,$ r$, and a constant $9.0\space \text{V}$ battery (no internal resistance). A student building this circuit wants to create a $6.0\space \text{V}$ potential difference across the variable resistor.

Which of the following values should the variable resistor have to meet this requirement?

A

${ 200 \space\Omega }$

B

${ 800 \space\Omega }$

C

${ 900 \space\Omega }$

D

${ 1600 \space\Omega }$

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