To determine the order of bulb brightness based on the currents, it is necessary to calculate the current for each given charge and time. Current ([tex]\(I\)[/tex]) is calculated using the formula:
[tex]\[ I = \frac{Q}{t} \][/tex]
where [tex]\(Q\)[/tex] is the charge in coulombs (C) and [tex]\(t\)[/tex] is the time in seconds (s).
Here are the steps to find the current for each given set of data:
1. For current [tex]\(W\)[/tex]:
[tex]\[
I_W = \frac{18 \text{ C}}{4.3 \text{ s}} = 4.186046511627907 \text{ A}
\][/tex]
2. For current [tex]\(X\)[/tex]:
[tex]\[
I_X = \frac{10 \text{ C}}{3.2 \text{ s}} = 3.125 \text{ A}
\][/tex]
3. For current [tex]\(Y\)[/tex]:
[tex]\[
I_Y = \frac{15 \text{ C}}{3.3 \text{ s}} = 4.545454545454546 \text{ A}
\][/tex]
4. For current [tex]\(Z\)[/tex]:
[tex]\[
I_Z = \frac{12 \text{ C}}{3.1 \text{ s}} = 3.8709677419354835 \text{ A}
\][/tex]
Now, we arrange these currents in descending order to determine the order of brightness, from most bright to least bright:
- [tex]\( I_Y = 4.545454545454546 \text{ A} \)[/tex]
- [tex]\( I_W = 4.186046511627907 \text{ A} \)[/tex]
- [tex]\( I_Z = 3.8709677419354835 \text{ A} \)[/tex]
- [tex]\( I_X = 3.125 \text{ A} \)[/tex]
Therefore, the order of currents from most bright to least bright is:
[tex]\[ Y, W, Z, X \][/tex]
The correct answer is:
[tex]\[ Y, W, Z, X \][/tex]
