Physics · Alternating Current
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The instantaneous current in a circuit is given by I = √2 sin(ωt + ∅) ampere what is the rms value of the current?
- A
2 A
- B
√2 A
- C
1 A
- D
(1/√2)A
The RMS (Root Mean Square) value of a sinusoidal alternating current is given by dividing the peak current by √2. For the given current I = √2 sin(ωt + ∅) A, the peak current I0 is √2 A. Thus, the RMS current is IRMS = I0/√2 = √2/√2 = 1 A. Therefore, the correct answer is 1 A. The other options are incorrect because they either represent the peak current or a miscalculated RMS value.
This option is incorrect. The RMS value is not directly equal to the peak value of the current.
This option is incorrect. The value given is the peak current, not the RMS current.
This is the correct option. The RMS value of a sinusoidal current, I = I0 sin(ωt + ∅), is I0/√2. Here, I0 = √2, so the RMS current is 1 A.
This option is incorrect. This value would represent the RMS of a peak current of 1 A, not √2 A.
Tagged under Physics · Alternating Current · 2018