In an LR𝐿𝑅 circuit connected to a battery, the rate at which the energy is stored in the inductor is plotted against time, during the growth of the current in the circuit. Which of the following best represents the resulting curve
Question
In an LR𝐿𝑅 circuit connected to a battery, the rate at which the energy is stored in the inductor is plotted against time, during the growth of the current in the circuit. Which of the following best represents the resulting curve
Solution
The rate at which energy is stored in an inductor in an LR circuit connected to a battery is given by the formula P = LIdI/dt, where P is power, L is inductance, I is current, and dI/dt is the rate of change of current with respect to time.
At the start, when the switch is first closed, the current is zero, so the power (and thus the rate of energy storage) is also zero. As time progresses, the current increases, and so does the rate of energy storage. However, as the current approaches its maximum value, its rate of change decreases, and so the rate of energy storage also decreases. Eventually, when the current reaches its maximum value and stops changing, the rate of energy storage drops to zero.
Therefore, the plot of the rate of energy storage against time starts at zero, increases to a maximum, and then decreases back to zero. This is typically represented by a bell-shaped curve.
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