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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
Solution
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
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