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
Top Questions on Electromagnetic induction
- The magnetic flux linked with a closed coil (in Wb) varies with time \( t \) (in s) as \( \phi = 5t^2 + 4t - 2 \). If the resistance of the circuit is 14 \( \Omega \), the magnitude of induced current in the coil at \( t = 1 \) s will be:
- CBSE CLASS XII - 2025
- Physics
- Electromagnetic induction
- The electric field in space between the plates of a parallel plate capacitor (each of area \( 2.5 \times 10^{-3} \, \text{m}^2 \)) is changing at the rate of \( 4 \times 10^6 \, \text{Vm}^{-1}\text{s}^{-1} \). The displacement current between the plates of the capacitor is :
- CBSE CLASS XII - 2025
- Physics
- Electromagnetic induction
- When current in a coil changes at a steady rate from 8 A to 6 A in 4 ms, an emf of 1.5 V is induced in it. The value of self-inductance of the coil is :
- CBSE CLASS XII - 2025
- Physics
- Electromagnetic induction
- State Lenz’s law and explain how this law is a consequence of conservation of energy principle.
- CBSE CLASS XII - 2025
- Physics
- Electromagnetic induction
- What will be the directions of induced current when the loop enters the field and when it leaves the field?
- CBSE CLASS XII - 2025
- Physics
- Electromagnetic induction
Questions Asked in JEE Main exam
- Let \( [x] \) denote the greatest integer function, and let \( m \) and \( n \) respectively be the numbers of the points, where the function \( f(x) = [x] + |x - 2| \), \( -2<x<3 \), is not continuous and not differentiable. Then \( m + n \) is equal to:
- JEE Main - 2025
- Differential Equations
- Let \( f(x) = \frac{x - 5}{x^2 - 3x + 2} \). If the range of \( f(x) \) is \( (-\infty, \alpha) \cup (\beta, \infty) \), then \( \alpha^2 + \beta^2 \) equals to.
- JEE Main - 2025
- Functions
- Let \( P_n = \alpha^n + \beta^n \), \( P_{10} = 123 \), \( P_9 = 76 \), \( P_8 = 47 \), and \( P_1 = 1 \). The quadratic equation whose roots are \( \frac{1}{\alpha} \) and \( \frac{1}{\beta} \) is:
- JEE Main - 2025
- Sequences and Series
- The value of \( (\sin 70^\circ)(\cot 10^\circ \cot 70^\circ - 1) \) is:
- JEE Main - 2025
- Trigonometric Identities
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:
- JEE Main - 2025
- Relations and functions
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