Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To determine how the current changes when the potential difference across a resistor increases by a factor of 4, we can analyze the situation using Ohm's law, which states [tex]\( V = I \cdot R \)[/tex].
Let's start by setting up the initial conditions and the subsequent change:
1. Initial setup:
- Let the initial voltage be [tex]\( V_{\text{initial}} \)[/tex].
- Let the initial current be [tex]\( I_{\text{initial}} \)[/tex].
- The resistance [tex]\( R \)[/tex] is calculated using Ohm's Law: [tex]\( R = \frac{V_{\text{initial}}}{I_{\text{initial}}} \)[/tex].
2. Change in voltage:
- The problem states that the potential difference (voltage) increases by a factor of 4.
- Therefore, the new voltage [tex]\( V_{\text{new}} \)[/tex] can be expressed as: [tex]\( V_{\text{new}} = 4 \cdot V_{\text{initial}} \)[/tex].
3. Determining the new current:
- Using Ohm's law again with the new voltage, we can solve for the new current [tex]\( I_{\text{new}} \)[/tex].
- Substituting [tex]\( V_{\text{new}} \)[/tex] and the resistance [tex]\( R \)[/tex], we get:
[tex]\[ V_{\text{new}} = I_{\text{new}} \cdot R \][/tex]
- Plugging in [tex]\( V_{\text{new}} = 4 \cdot V_{\text{initial}} \)[/tex] and [tex]\( R = \frac{V_{\text{initial}}}{I_{\text{initial}}} \)[/tex]:
[tex]\[ 4 \cdot V_{\text{initial}} = I_{\text{new}} \cdot \frac{V_{\text{initial}}}{I_{\text{initial}}} \][/tex]
- Simplifying the equation:
[tex]\[ 4 \cdot V_{\text{initial}} = I_{\text{new}} \cdot \frac{V_{\text{initial}}}{I_{\text{initial}}} \][/tex]
[tex]\[ I_{\text{new}} = 4 \cdot I_{\text{initial}} \][/tex]
4. Conclusion:
- The new current is [tex]\( 4 \)[/tex] times the initial current.
Therefore, the current increases by a factor of 4 when the potential difference increases by a factor of 4. This corresponds to option B.
Final Answer: B. It increases by a factor of 4.
Let's start by setting up the initial conditions and the subsequent change:
1. Initial setup:
- Let the initial voltage be [tex]\( V_{\text{initial}} \)[/tex].
- Let the initial current be [tex]\( I_{\text{initial}} \)[/tex].
- The resistance [tex]\( R \)[/tex] is calculated using Ohm's Law: [tex]\( R = \frac{V_{\text{initial}}}{I_{\text{initial}}} \)[/tex].
2. Change in voltage:
- The problem states that the potential difference (voltage) increases by a factor of 4.
- Therefore, the new voltage [tex]\( V_{\text{new}} \)[/tex] can be expressed as: [tex]\( V_{\text{new}} = 4 \cdot V_{\text{initial}} \)[/tex].
3. Determining the new current:
- Using Ohm's law again with the new voltage, we can solve for the new current [tex]\( I_{\text{new}} \)[/tex].
- Substituting [tex]\( V_{\text{new}} \)[/tex] and the resistance [tex]\( R \)[/tex], we get:
[tex]\[ V_{\text{new}} = I_{\text{new}} \cdot R \][/tex]
- Plugging in [tex]\( V_{\text{new}} = 4 \cdot V_{\text{initial}} \)[/tex] and [tex]\( R = \frac{V_{\text{initial}}}{I_{\text{initial}}} \)[/tex]:
[tex]\[ 4 \cdot V_{\text{initial}} = I_{\text{new}} \cdot \frac{V_{\text{initial}}}{I_{\text{initial}}} \][/tex]
- Simplifying the equation:
[tex]\[ 4 \cdot V_{\text{initial}} = I_{\text{new}} \cdot \frac{V_{\text{initial}}}{I_{\text{initial}}} \][/tex]
[tex]\[ I_{\text{new}} = 4 \cdot I_{\text{initial}} \][/tex]
4. Conclusion:
- The new current is [tex]\( 4 \)[/tex] times the initial current.
Therefore, the current increases by a factor of 4 when the potential difference increases by a factor of 4. This corresponds to option B.
Final Answer: B. It increases by a factor of 4.
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.