Question

Consider an AC circuit consisting of a power supply and a resistor. If the current in the circuit at time t is /, then the power delivered to the resistor is /, where R is the resistance. Express the power in terms of .

Answer 1

B on Edge

Explanation:

Got it right on the test

Answer 2

Option B. is the answer.

Explanation:

The given question is incomplete; complete question has been given in the picture attached.

Current in the circuit at the time t is
`I_(0)sinwt`.

Power delivered to the resistor is
`I_(0)Rsin^(2)wt`

Where R = resistance

We have to express the power in the terms of cos2w.

Since formula to get the power in a circuit with resistance R and current I is given by

P = I²R

Therefore, power for the given circuit will be

P =
`(I_(0))^(2) Rsin^(2)wt`

P =
`I^(2)_(0)R((1-cos2wt)/(2))` [Since sin²t =
`(1-sin^(2)wt)/(2)`]

P =
`(I^(2)_(0)R)/(2)-(1)/(2)I^(2)_(0)cos2wt`

Therefore, Option B. will be the answer.