Question

In an AC circuit, e and i are given by e = 150 sin(150t)V and i = 150 sin `(150t + π/3)` A. The power dissipated in the circuit is ______.

Options

• 106W

• 150W

• 5625W

• Zero

Answer 1

In an AC circuit, e and i are given by e = 150 sin(150t)V and i = 150 sin `(150t + π/3)` A. The power dissipated in the circuit is 5625W.

Explanation:

Let, Voltage supplied  = V = `150 sin(150t)` .....(1)

Current flowing = I = `150 sin(150t + pi/3)`  .....(2)

∵ `V = V_0 sin(wt)`

So, on comparing it with (1), we get

`V_0 = 150V`  .....(3)

Also,

∵ `I = I_0 sin(wt + phi)`

So, on comparing it with (2), we get

`I_0 = 150A`  ....(4)

`phi = pi/3`  .....(5)

As, the power in the AC circuit is given by:

`P = 1/2V_0I_0 cos phi`  ....(6)

Put the values in equations (3), (4), (5) and (6) and calculate:

∴ `P = 1/2 xx 150 xx 150 xx cos 60`

P = 5625W