To solve this problem, we need to understand the relationship between the electromotive force (EMF) and the current. We are told that the force is proportional to the current, which implies that as the current increases, the force increases as well, maintaining a constant ratio.
Given:
- Initial current ([tex]\( I_{\text{initial}} \)[/tex]) = 10 A
- Initial electromotive force ([tex]\( F_{\text{initial}} \)[/tex]) = 50 V
- New current ([tex]\( I_{\text{new}} \)[/tex]) = 25 A
Since the electromotive force is proportional to the current, we can set up a ratio of the initial conditions and the new conditions:
[tex]\[ \frac{F_{\text{initial}}}{I_{\text{initial}}} = \frac{F_{\text{new}}}{I_{\text{new}}} \][/tex]
We need to find the new force ([tex]\( F_{\text{new}} \)[/tex]). Rearranging the equation to solve for [tex]\( F_{\text{new}} \)[/tex]:
[tex]\[ F_{\text{new}} = \frac{I_{\text{new}} \cdot F_{\text{initial}}}{I_{\text{initial}}} \][/tex]
Substituting the given values into the equation:
[tex]\[ F_{\text{new}} = \frac{25 \, \text{A} \cdot 50 \, \text{V}}{10 \, \text{A}} \][/tex]
Now, perform the calculation:
[tex]\[ F_{\text{new}} = \frac{1250 \, \text{V} \cdot \text{A}}{10 \, \text{A}} \][/tex]
[tex]\[ F_{\text{new}} = 125 \, \text{V} \][/tex]
So, the new electromotive force when the current is 25 A is 125 V.
