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Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework-like questions.

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Why is this circuit component on without a potential difference?

Bulb H is connected to second battery directly. As long as this bulb is not short circuited, there will be some applied potential difference across its terminals and hence it will be ON
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