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Solve the Problem P=RI2\mathrm { P } = \mathrm { RI } ^ { 2 }

question 204

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Solve the problem.
-The power dissipated in an electric circuit is given by the expression P=RI2\mathrm { P } = \mathrm { RI } ^ { 2 } , where R\mathrm { R } is the resistance of the circuit and I\mathrm { I } is the current through the circuit. For a sinusoidal alternating current, the current might be represented by the relation I=Asin(2πft) \mathrm { I } = \mathrm { A } \sin ( 2 \pi \mathrm { ft } ) , where A\mathrm { A } is the amplitude, f\mathrm { f } is the frequency, and tt is time. Write an expression for P involving the sine function, and use a fundamental identity to write PP in terms of the cosine function.


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