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

question 204

Multiple Choice

Solve the problem.
-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 $t$ is time. Write an expression for P involving the sine function, and use a fundamental identity to write $P$ in terms of the cosine function.

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

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Definitions:

Target Payout Ratio

The target payout ratio is a company’s long-term goal for the percentage of its earnings that will be paid out to shareholders as dividends.

Residual

The remaining value of an asset after depreciation or the remaining amount after all deductions have been made.

Cash Dividend

Payment made by a company out of its earnings to shareholders in the form of cash, representing a share of the corporate profits.

Decrease in Dividends

A reduction in the amount paid out to shareholders from a company's earnings, often signaling a change in financial health or strategy.