10) If the voltage, V, in an electric circuit is held constant, the current, I, is inversely proportional to the resistance, R. If the current is 350 milliamperes when the resistance is 5 ohms, find the current when the resistance is 35 ohms.
10) If the voltage, V, in an electric circuit is held constant, the current, I, is inversely proportional to the resistance, R. If the current is 350 milliamperes when the resistance is 5 ohms, find the current when the resistance is 35 ohms.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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Author:Bruce Crauder, Benny Evans, Alan Noell
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Please assist in this intermediate algebra problem. This chapter is on polynomials and rationals
![### Problem 10: Electrical Circuit Analysis
**Question:**
If the voltage, \( V \), in an electric circuit is held constant, the current, \( I \), is inversely proportional to the resistance, \( R \). If the current is 350 milliamperes when the resistance is 5 ohms, find the current when the resistance is 35 ohms.
**Solution:**
To solve this problem, we need to use the concept of Ohm's Law and the relationship between current and resistance, given that the voltage is constant.
#### Step-by-step Solution:
1. **Understand that Current is Inversely Proportional to Resistance:**
The relationship can be expressed as:
\[
I \propto \frac{1}{R}
\]
Which means:
\[
I = \frac{k}{R}
\]
where \( k \) is a constant.
2. **Determine the Constant \( k \):**
We know from the problem statement that:
\[
I = 350 \text{ mA} \quad \text{when} \quad R = 5 \text{ ohms}
\]
So we can substitute these values into the equation to find \( k \):
\[
350 = \frac{k}{5}
\]
Solving for \( k \), we get:
\[
k = 350 \times 5 = 1750
\]
3. **Find the Current for \( R = 35 \text{ ohms} \):**
Using the relationship from step 1 and the value of \( k \) we calculated, we substitute \( R = 35 \):
\[
I = \frac{1750}{35}
\]
Simplifying, we get:
\[
I = 50 \text{ mA}
\]
So, the current when the resistance is 35 ohms is **50 milliamperes**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a79e915-3d5c-4c79-9ba5-7a5ef81967b7%2F9eb91051-d31f-4b50-980c-577e997f3fe7%2Fz8fk0gl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 10: Electrical Circuit Analysis
**Question:**
If the voltage, \( V \), in an electric circuit is held constant, the current, \( I \), is inversely proportional to the resistance, \( R \). If the current is 350 milliamperes when the resistance is 5 ohms, find the current when the resistance is 35 ohms.
**Solution:**
To solve this problem, we need to use the concept of Ohm's Law and the relationship between current and resistance, given that the voltage is constant.
#### Step-by-step Solution:
1. **Understand that Current is Inversely Proportional to Resistance:**
The relationship can be expressed as:
\[
I \propto \frac{1}{R}
\]
Which means:
\[
I = \frac{k}{R}
\]
where \( k \) is a constant.
2. **Determine the Constant \( k \):**
We know from the problem statement that:
\[
I = 350 \text{ mA} \quad \text{when} \quad R = 5 \text{ ohms}
\]
So we can substitute these values into the equation to find \( k \):
\[
350 = \frac{k}{5}
\]
Solving for \( k \), we get:
\[
k = 350 \times 5 = 1750
\]
3. **Find the Current for \( R = 35 \text{ ohms} \):**
Using the relationship from step 1 and the value of \( k \) we calculated, we substitute \( R = 35 \):
\[
I = \frac{1750}{35}
\]
Simplifying, we get:
\[
I = 50 \text{ mA}
\]
So, the current when the resistance is 35 ohms is **50 milliamperes**.
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