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"if we put a voltagel across $i$ and $j$, then
$k$ and $l$ being identical implies that they are at the same
potential."
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If there is an applied potential difference between i and j, the potential difference between k and l is the same, owing to $k$ and $l$ being identical.
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If i and j to add between voltage, k and l is the equivalent of suggesting that they have the same voltage.
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