V=-2.6+(d)/(3) The electric potential, V, in volts, between two metal plates a distance of d millimeters from the left plate is given by the equation when 0 <= d <= 15. By how many millimeters does the distance from the left plate increase for the potential to increase by 1 volt?

Understanding electric potential: Understand the relationship between electric potential and distance. The electric potential V is given by the equation V = -2.6 + (d/3), where d is the distance in millimeters from the left plate. We need to find out how much d needs to increase for V to increase by 1 volt.Setting up the equation for potential increase: Set up the equation for the increase in potential. Let's say the potential increases by 1 volt, so the change in V, which we can call ΔV, is 1 volt. We want to find the change in distance, Δd, that corresponds to this change in potential. The new potential after the increase will be V + ΔV.Writing the equation for the new potential: Write the equation for the new potential. The new potential after the increase is V + 1 = -2.6 + (d + Δd)/3. We need to solve this equation for Δd.Substituting the original potential: Substitute the original potential into the new equation. We know that the original potential is V = -2.6 + d/3. So, we can substitute V into the new equation: V + 1 = V + (Δd/3).Simplifying the equation to solve for Δd: Simplify the equation to solve for Δd. Since V on both sides of the equation cancels out, we are left with 1 = Δd/3. To find Δd, we multiply both sides of the equation by 3.Calculating the change in distance Δd: Calculate the change in distance Δd. Multiplying both sides of the equation by 3 gives us Δd = 3 * 1, which means Δd = 3 millimeters.

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V=-2.6+(d)/(3)
The electric potential,
V, in volts, between two metal plates a distance of
d millimeters from the left plate is given by the equation when
0 <= d <= 15. By how many millimeters does the distance from the left plate increase for the potential to increase by 1 volt?

$V=-2.6+\frac{d}{3}$ $\newline$ The electric potential, $V$ , in volts, between two metal plates a distance of $d$ millimeters from the left plate is given by the equation when $0 \leq d \leq 15$ . By how many millimeters does the distance from the left plate increase for the potential to increase by $1$ volt?

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V=-2.6+\frac{d}{3}

\newline

The electric potential,

V

, in volts, between two metal plates a distance of

d

millimeters from the left plate is given by the equation when

0 \leq d \leq 15

. By how many millimeters does the distance from the left plate increase for the potential to increase by

1

volt?

Understanding electric potential: Understand the relationship between electric potential and distance. $\newline$ The electric potential $V$ is given by the equation $V = -2.6 + \frac{d}{3}$ , where $d$ is the distance in millimeters from the left plate. We need to find out how much $d$ needs to increase for $V$ to increase by $1$ volt.
Setting up the equation for potential increase: Set up the equation for the increase in potential. $\newline$ Let's say the potential increases by $1$ volt, so the change in $V$ , which we can call $\Delta V$ , is $1$ volt. We want to find the change in distance, $\Delta d$ , that corresponds to this change in potential. The new potential after the increase will be $V + \Delta V$ .
Writing the equation for the new potential: Write the equation for the new potential. $\newline$ The new potential after the increase is $V + 1 = -2.6 + \frac{d + \Delta d}{3}$ . We need to solve this equation for $\Delta d$ .
Substituting the original potential: Substitute the original potential into the new equation. $\newline$ We know that the original potential is $V = -2.6 + \frac{d}{3}$ . So, we can substitute $V$ into the new equation: $V + 1 = V + \left(\frac{\Delta d}{3}\right)$ .
Simplifying the equation to solve for $\Delta d$ : Simplify the equation to solve for $\Delta d$ . Since $V$ on both sides of the equation cancels out, we are left with $1 = \frac{\Delta d}{3}$ . To find $\Delta d$ , we multiply both sides of the equation by $3$ .
Calculating the change in distance $\Delta d$ : Calculate the change in distance $\Delta d$ . $\newline$ Multiplying both sides of the equation by $3$ gives us $\Delta d = 3 \times 1$ , which means $\Delta d = 3$ millimeters.