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Q. 70

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 741

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Short Answer

The current that charges a capacitor transfers energy that is stored in the capacitor's electric field. Consider a capacitor, initially uncharged, that is storing energy at a constant rate. What is the capacitor voltage after charging begins?

The capacitor voltage will be after charging begins at .

See the step by step solution

Step by Step Solution

Step 1: Given Information

Capacitor

Storing energy rate

Time

Step 2: Explanation

The expression of capacitance will be,

using the definition of current

Just as in the previous exercise. As a result, we can give the increase in the potential difference using the current differential and dime differential

Keeping in mind that the product of the intensity and the current is the power, this means we can express the intensity as the product of the intensity and the current.

This means that our equation for the infinitesimal increase in potential difference will become

Throwing the potential difference on the other side, we get

Step 3: Explanation

Integrate both sides,

Getting back to our example, if the capacitor hasn't been charged (to calculate the potential difference at time 0), there will be no constant at the end of the integration. This means that the potential difference can be expressed in the following way:

In our numerical case, we will have

Multiply the values,

Step 3: Final Answer

Hence, the capacitor voltage will be after charging begins at

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