Decide Whether the Expression Is or Is Not an Identity $\mathrm { P } = \mathrm { RI } ^ { 2 }$

question 242

Multiple Choice

Decide whether the expression is or is not an identity.
-The power dissipated in an electric circuit is given by the expression $\mathrm { P } = \mathrm { RI } ^ { 2 }$ , where $\mathrm { R }$ is the resistance of the circuit and $\mathrm { I }$ is the current through the circuit. For a sinusoidal alternating current, the current might be represented by the relation $\mathrm { I } = \mathrm { A } \sin ( 2 \pi \mathrm { ft } )$ , where $\mathrm { A }$ is the amplitude, $\mathrm { f }$ is the frequency, and $\mathrm { t }$ is time. Write an expression for $\mathrm { P }$ involving the sine function, and use a fundamental identity to write $\mathrm { P }$ in terms of the cosine function.

• A) \(P = R A \sin ^ { 2 } ( 2 \pi f t ) ; P = R A - R A \cos ^ { 2 } ( 2 \pi f t )\)
• B) \(\mathrm { P } = \mathrm { RA } ^ { 2 } \sin ^ { 2 } ( 2 \pi \mathrm { ft } ) ; \mathrm { P } = - \mathrm { RA } ^ { 2 } \cos ^ { 2 } ( 2 \pi \mathrm { ft } )\)
• C) \(P = R A \sin ^ { 2 } ( 2 \pi \mathrm { ft } ) ; P = R A - \cos ^ { 2 } ( 2 \pi f t )\)
• D) \(\mathrm { P } = \mathrm { RA } ^ { 2 } \sin ^ { 2 } ( 2 \pi \mathrm { ft } ) ; \mathrm { P } = \mathrm { RA } ^ { 2 } - \mathrm { RA } ^ { 2 } \cos ^ { 2 } ( 2 \pi \mathrm { ft } )\)

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