Answer:
[tex]\displaystyle \frac{1}{4}[/tex].
Step-by-step explanation:
The voltage across the three bulbs would add up to [tex]12\; {\rm V}[/tex] since the three bulbs are connected in serial.
The voltage across the third bulb would thus be: [tex]12\; {\rm V} - 6\; {\rm V} - 3\; {\rm V} = 3\; {\rm V}[/tex].
Also because the three bulbs are connected in serial, the current going through each of them be the same as the size of the current of the whole circuit. Let [tex]I\; {\rm A}[/tex] be the size of that current.
- The power supplied by the battery would be [tex]P = V \, I = 12\; {\rm V} \, (I\; {\rm A}) = (12\, I)\; {\rm W}[/tex].
- The power of the third bulb would be [tex]P = V\, I = 3\; {\rm V} \, (I\; {\rm A}) = (3\, I)\; {\rm W}[/tex].
Thus, the portion of the power consumed by the third bulb would be [tex](3\, I) / (12\, I) = 1/4[/tex].
