Which of the following changes will increase the energy stored in the capacitor in the lightning circuit model by the greatest amount?A.Increasing C by a factor of 2B.Decreasing C by a factor of 2C.Increasing V by a factor of 2D.Decreasing V by a factor of 2Submit
Question
Which of the following changes will increase the energy stored in the capacitor in the lightning circuit model by the greatest amount?A.Increasing C by a factor of 2B.Decreasing C by a factor of 2C.Increasing V by a factor of 2D.Decreasing V by a factor of 2Submit
Solution
The energy stored in a capacitor is given by the formula E = 1/2 * C * V^2, where E is the energy, C is the capacitance, and V is the voltage.
A. Increasing C by a factor of 2: This would double the energy stored in the capacitor, since the energy is directly proportional to the capacitance.
B. Decreasing C by a factor of 2: This would halve the energy stored in the capacitor, since the energy is directly proportional to the capacitance.
C. Increasing V by a factor of 2: This would quadruple the energy stored in the capacitor, since the energy is proportional to the square of the voltage.
D. Decreasing V by a factor of 2: This would reduce the energy stored in the capacitor to one-fourth, since the energy is proportional to the square of the voltage.
Therefore, the change that will increase the energy stored in the capacitor by the greatest amount is C. Increasing V by a factor of 2.
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