To find the current \(x\) that produces maximum power in the function \(P(x) = -12x^2 + 120x\), we need to determine the vertex of the parabola represented by this quadratic equation. The standard form of a quadratic function is given by:
\[ P(x) = ax^2 + bx + c \]
In this case:
- \(a = -12\)
- \(b = 120\)
The x-coordinate of the vertex can be found using the formula:
\[ x = -\frac{b}{2a} \]
Substituting in the values of \(a\) and \(b\):
\[ x = -\frac{120}{2 \cdot -12} = -\frac{120}{-24} = 5 \]
Thus, the current that will produce the maximum power is
\[ \boxed{5} \text{ amperes}. \]
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