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Q. 69

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

69. II The current through inductance is given by .

CALC a. Find an expression for the potential difference across the inductor.

b. The maximum voltage across the inductor is when and . What is ?

Part (a) The expression for potential difference across the inductor is

Part (b) The maximum voltage across the inductor is

See the step by step solution

Step by Step Solution

Part (a)

The current in the inductor at any instant of time is

Here, is the angular frequency, is the time taken by the current in the inductor, and is the maximum current in the inductor.

Differentiate the equation with respect to time .

The potential difference across the inductance is

Therefore, the expression for potential difference across the inductor is

Part (b)

Convert the units for inductance from to .

Convert the units for frequency from to

The maximum cosine value varies from +1 to -1 . So the maximum potential difference across the inductor is,

Rewrite the equation for current

Therefore, the maximum voltage across the inductor is

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