A resistance of 40 Ω is connected to a source of alternating current rated 220 V, 50 Hz. Find the time taken by the current to change from its maximum value to the rms value :
A resistance of 40 Ω is connected to a source of alternating current rated 220 V, 50 Hz. Find the time taken by the current to change from its maximum value to the rms value :
- 2.5 ms
- 1.25 ms
- 2.5 s
- 0.25 s
The Correct Option is A
Solution and Explanation
I = I0cos(ωt) say
⇒ At maximum ωt1 = 0 or t1 = 0
Then at rms value
l=l0l√2
⇒ ωt2 = \(\frac{\pi}{4}\)
⇒ ω(t2 – t1) = \(\frac{\pi}{4}\)
Δt=\(\frac{\pi}{4}\)ω=\(\frac{\pi T}{4}\)×2π
=\(\frac{1}{400}\) s or 2.5 ms
The correct option is (A) : 2.5 ms
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Concepts Used:
Electromagnetic Induction
Electromagnetic Induction is a current produced by the voltage production due to a changing magnetic field. This happens in one of the two conditions:-
- When we place the conductor in a changing magnetic field.
- When the conductor constantly moves in a stationary field.
Formula:
The electromagnetic induction is mathematically represented as:-
e=N × d∅.dt
Where
- e = induced voltage
- N = number of turns in the coil
- Φ = Magnetic flux (This is the amount of magnetic field present on the surface)
- t = time
Applications of Electromagnetic Induction
- Electromagnetic induction in AC generator
- Electrical Transformers
- Magnetic Flow Meter