Question
Use a variation model to solve for the unknown value.
The current in a wire varies directly as the voltage and inversely as the resistance. If the current is 16 amperes (A) when the voltage is 75 volts (V) and the resistance is 15 ohms (52), find the current when the voltage is 170 V and the resistance is 13 %.
The current in a wire varies directly as the voltage and inversely as the resistance. If the current is 16 amperes (A) when the voltage is 75 volts (V) and the resistance is 15 ohms (52), find the current when the voltage is 170 V and the resistance is 13 %.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
The relationship given in the problem states that the current \( I \) varies directly as the voltage \( V \) and inversely as the resistance \( R \). This can be represented mathematically as:
\[
I = k \frac{V}{R}
\]
where \( k \) is a constant of proportionality.
### Step 1: Find the constant \( k \)
Using the initial conditions: \( I = 16 \, A \), \( V = 75 \, V \), and \( R = 15 \, \Omega \):
\[
16 = k \frac{75}{15}
\]
Calculating the fraction:
\[
\frac{75}{15} = 5
\]
Substituting back into the equation:
\[
16 = k \cdot 5
\]
Now solve for \( k \):
\[
k = \frac{16}{5} = 3.2
\]
### Step 2: Find the current for the new conditions
Now we can use this value of \( k \) to find the current when \( V = 170 \, V \) and \( R = 13 \, \Omega \):
\[
I = 3.2 \frac{170}{13}
\]
Calculating the fraction \( \frac{170}{13} \):
\[
\frac{170}{13} \approx 13.07692307
\]
Now substituting this back:
\[
I = 3.2 \times 13.07692307
\]
Calculating the final result:
\[
I \approx 41.15384615
\]
Rounding to a reasonable number of significant figures, the current is approximately:
\[
\boxed{41.15 \, A}
\]
Thus, the current when the voltage is 170 V and the resistance is 13 Ohms is approximately 41.15 amperes.
\[
I = k \frac{V}{R}
\]
where \( k \) is a constant of proportionality.
### Step 1: Find the constant \( k \)
Using the initial conditions: \( I = 16 \, A \), \( V = 75 \, V \), and \( R = 15 \, \Omega \):
\[
16 = k \frac{75}{15}
\]
Calculating the fraction:
\[
\frac{75}{15} = 5
\]
Substituting back into the equation:
\[
16 = k \cdot 5
\]
Now solve for \( k \):
\[
k = \frac{16}{5} = 3.2
\]
### Step 2: Find the current for the new conditions
Now we can use this value of \( k \) to find the current when \( V = 170 \, V \) and \( R = 13 \, \Omega \):
\[
I = 3.2 \frac{170}{13}
\]
Calculating the fraction \( \frac{170}{13} \):
\[
\frac{170}{13} \approx 13.07692307
\]
Now substituting this back:
\[
I = 3.2 \times 13.07692307
\]
Calculating the final result:
\[
I \approx 41.15384615
\]
Rounding to a reasonable number of significant figures, the current is approximately:
\[
\boxed{41.15 \, A}
\]
Thus, the current when the voltage is 170 V and the resistance is 13 Ohms is approximately 41.15 amperes.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.