Integration help

Question

Answer 1

Step 1:

Alternating sinusoidal current function is .

Where, is amplitude, is the time and is the phase.

For alternating current, the differential amount of heat  by joule-lenz law is .

Find the quantity of heat released by alternating sinusoidal current during a cycle in a conductor by integrating above expression.

.

Substitute in above expression.

Step 2:

Double angle  identity: .

Therefore, heat released by alternating sinusoidal current during a cycle in a conductor is .

Solution:

Heat released by alternating sinusoidal current during a cycle in a conductor is .

Comments

Please explain:

 

 

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Consider .

Rewrite the expression as .

Trigonometric property: .

Trigonometric property: .

.

Hence