If a battery is running down, a light bulb in the circuit will become dimmer because when voltage drops
a. there's less current flowing through the bulb.
b. the resistance in the circuit increases proportionally.
c. the circuit that was once closed is starting to open some.
d. there's the same amount of current flowing but it's not flowing as fast.

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wboast
A. There is less current flowing through the bulb.

Ohms law dictates that Electrical voltage = current x resistance. To understand current you would divide voltage by resistance. The less voltage the less current will run through the circuit.

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