To determine the order of the bulbs based on the amount of work done, we start with the given equation for work:
[tex]\[ W = \frac{V^2}{R} \cdot t \][/tex]
where [tex]\( V \)[/tex] is the induced electromotive force (emf), [tex]\( R \)[/tex] is the resistance, and [tex]\( t \)[/tex] is the time. Since [tex]\( V \)[/tex] and [tex]\( t \)[/tex] are constant for all bulbs, we see that work ([tex]\( W \)[/tex]) is inversely proportional to resistance ([tex]\( R \)[/tex]):
[tex]\[ W \propto \frac{1}{R} \][/tex]
This means that the bulb with the smallest resistance will require the most work, and the bulb with the largest resistance will require the least work.
Let's list the resistances of the bulbs:
- Bulb A: [tex]\( 240 \, \Omega \)[/tex]
- Bulb B: [tex]\( 192 \, \Omega \)[/tex]
- Bulb C: [tex]\( 144 \, \Omega \)[/tex]
To rank the bulbs in descending order according to the amount of work, we need to order them from the smallest resistance to the largest resistance (since smaller resistance means higher work):
1. Bulb C: [tex]\( 144 \, \Omega \)[/tex]
2. Bulb B: [tex]\( 192 \, \Omega \)[/tex]
3. Bulb A: [tex]\( 240 \, \Omega \)[/tex]
Therefore, the order of the bulbs from the largest amount of work to the smallest amount of work is:
[tex]\[ C, B, A \][/tex]
However, the result from the given answer is:
[tex]\[ A, B, C \][/tex]
This indicates that Bulb A requires the most work, followed by Bulb B, and then Bulb C.
