How is the current related to the wire resistance when the voltage of the battery remains constant? Is it directly or inversely related? Please explain your answer.
How is the current related to the wire resistance when the voltage of the battery remains constant? Is it directly or inversely related? Please explain your answer.
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Chapter1: Units, Trigonometry. And Vectors
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![**Question:**
How is the current related to the wire resistance when the voltage of the battery remains constant? Is it directly or inversely related? Please explain your answer.
**Answer:**
In electrical circuits, Ohm's Law describes the relationship between voltage (V), current (I), and resistance (R). Specifically, Ohm's Law is expressed as:
\[ V = I \times R \]
Where:
- \( V \) is the voltage,
- \( I \) is the current,
- \( R \) is the resistance.
Given that the voltage \( V \) of the battery remains constant, the current \( I \) is related to the resistance \( R \) by re-arranging Ohm's Law:
\[ I = \frac{V}{R} \]
From this equation, it can be observed that the current \( I \) is inversely related to the resistance \( R \). This means that as the resistance increases, the current decreases and vice versa, provided the voltage remains unchanged.
**Explanation:**
- Directly related means that if one quantity increases, the other also increases. Conversely, inversely related means that if one quantity increases, the other decreases.
- In this case, since \( I = \frac{V}{R} \), as the resistance \( R \) increases, the fraction \( \frac{V}{R} \) decreases, leading to a lower current \( I \).
Therefore, when the voltage of the battery remains constant, the current is **inversely related** to the wire resistance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23c38651-d5a3-4c38-ab9e-97c20b9d1405%2Fe868cd49-1aad-4232-a87e-539a5d3b2c07%2F4wholh_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
How is the current related to the wire resistance when the voltage of the battery remains constant? Is it directly or inversely related? Please explain your answer.
**Answer:**
In electrical circuits, Ohm's Law describes the relationship between voltage (V), current (I), and resistance (R). Specifically, Ohm's Law is expressed as:
\[ V = I \times R \]
Where:
- \( V \) is the voltage,
- \( I \) is the current,
- \( R \) is the resistance.
Given that the voltage \( V \) of the battery remains constant, the current \( I \) is related to the resistance \( R \) by re-arranging Ohm's Law:
\[ I = \frac{V}{R} \]
From this equation, it can be observed that the current \( I \) is inversely related to the resistance \( R \). This means that as the resistance increases, the current decreases and vice versa, provided the voltage remains unchanged.
**Explanation:**
- Directly related means that if one quantity increases, the other also increases. Conversely, inversely related means that if one quantity increases, the other decreases.
- In this case, since \( I = \frac{V}{R} \), as the resistance \( R \) increases, the fraction \( \frac{V}{R} \) decreases, leading to a lower current \( I \).
Therefore, when the voltage of the battery remains constant, the current is **inversely related** to the wire resistance.
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