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The table lists the time it takes for an amount of charge to pass through a point in a wire.

\begin{tabular}{|c|c|c|}
\hline Current & Charge (C) & Time (s) \\
\hline W & 18 & 4.3 \\
\hline X & 10 & 3.2 \\
\hline Y & 15 & 3.3 \\
\hline Z & 12 & 3.1 \\
\hline
\end{tabular}

Janelle is exploring the relationship between the brightness of a light bulb and the current that powers it. When applying these currents to the same bulb, the bulb is brighter when the current is greater.

Which lists the currents in the order of the bulb brightness they cause, from most bright to least bright?

A. [tex]$W, Y, X, Z$[/tex]
B. [tex]$Y, W, Z, X$[/tex]
C. [tex]$W, Y, Z, X$[/tex]
D. [tex]$X, Z, W, Y$[/tex]

Sagot :

GinnyAnswer
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]
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