At which position of the plane of the rotating coil with the direction of magnetic field, the e.m.f. induced in the coil is maximum?

Equation for induced emf is given by the following relation, e = N B A ω sin ω t For induced emf to be maximum, sin ω t should be maximum. sin ω t = 1 is the maximum value. Then, ω t = 90 ° Hence at 90 ° induced emf will be maximum.

Prove theoretically, the relation between e.m.f induced in a coil and rate of change of magnetic flux in electromagnetic induction.

From the above diagram, the area of the loop inside the magnetic field is, A = l x . Let the magnitude of the magnetic field is B . Hence, the flux is given by, ϕ = B A = B l x . Let us see what the time derivative of the flux means, d ϕ d t = d B l x d t = B l d x d t = - B l v . . . . . ( 1 ) d x d t = - v because the value of x is decreasing with time. Take a unit charge in the section A B . It is moving horizontally with a speed of v . Hence, from Lorentz law, the force acting on it will be, F = v B . From right-hand thumb rule, the direction can be found to be upwards. We know that the e.m.f of a cell is defined as the work done by the internal forces of the cell on a unit charge to bring it from the negative plate to the positive plate. Hence, the induced EMF will be equal to the work done by on the unit charge i.e., e . m . f = F l = B v l . . . . . ( 2 ) Note that the work done on the unit charge as it moves along A D or C B is zero, as the force is perpendicular to A D and C B . By comparing the above two equations, one can say that the induced e.m.f is nothing but the negative of rate of change of flux.

What does the negative sign indicate in Lenz’s law?

The negative sign indicates that the induced EMF is in such a way that it opposes the flux change caused. This is in agreement with the law of conservation of energy. According to Faraday's Law: E = - d ϕ d t

A capacitor of capacitance 0 . 5 μF is connected to a source of alternating e.m.f. of frequency 100 Hz . What is the capacitive reactance? ( π = 3 . 142 )

Given: The capacitance of the capacitor, C = 0 . 5 μF . The frequency of the source of alternating emf, f = 100 Hz . The capacitive reactance of the capacitor, X C = 1 ω C = 1 2 π f C = 1 2 π × 100 × 0 . 5 × 10 - 6 = 10 - 4 3 . 142 = 31 . 82 μΩ .

If a coil of metal wire is kept stationary in a uniform magnetic field, then_______.

Neither e.m.f. nor current is induced.

An e.m.f. is induced in the coil.

A current is induced in the coil.

Both current and e.m.f. are induced.

Assuming expression for impedance in a parallel resonant circuit, state the conditions for parallel resonance. Define resonant frequency and obtain an expression for it.

Refer to the diagrams given below: e Z = e X c - e X L ⇒ 1 Z = 1 X c - 1 X L U n d e r r e s o n a n c e c o n d i t i o n X c = X L 1 Z = 0 ⇒ Z = ∞ This frequency is called resonant frequency, at this frequency the impedance is minimum. The resonance frequency is obtained as: ω C = 1 ω L ⇒ ω 2 = 1 L C ⇒ ω = 1 L C