Prove Theoretically the Relation Between E.M.F. Induced in a Coil and Rate of Change of Magnetic Flux in Electromagnetic Induction. - Physics

Advertisements
Advertisements
Answer in Brief

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

Advertisements

Solution

1) 

Magnetic flux Φ = NABcos ωt

N → No.s of turns

A → Area of a coil

B → Magnetic field {external}

ω → Angular speed of the coil

`:. max phi_0 = NAB, omegat -> 0`

`:.phi = phi_0 cos omegat`

induce EMF(e)

e = `-(dphi)/(dt) = + omegaNAB sin omegat`

`e_0 = omegaNAB, omegat -> 90`

`:. e = e_0 sin omegat`

So there is phase difference of `pi/2` with `phi` and e

  Is there an error in this question or solution?
2017-2018 (March)

APPEARS IN

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

An alternating emf of 220 V is applied to a circuit containing a resistor R having the resistance of 160Ω and a capacitor ‘C’ is series. The current is found to lead the supply voltage by an angle

`θ = tan^(-1) ("3/4")`

a) Calculate

1) The capacitive reactance

2) The impedance of the circuit

3) Current flowing in the circuit

b) If the frequency of the applied emf is 50 Hz, what is the value of the capacitance of the capacitor ‘C’?


An A.C. generator generating an emf of ε = 300 sin (100 πt) V is connected to a series combination of 16μ F capacitor, 1 H inductor and 100 Ω resistor.

Calculate :

1) An impedance of the circuit at the given frequency.

2) Resonant frequency `f_0`

3)Power factor at the resonant frequency `f_0`.


Define the quality factor in an a.c. circuit. Why should the quality factor have high value in receiving circuits? Name the factors on which it depends.


In a circuit, containing a capacitor and an AC source, the current is zero at the instant the source voltage is maximum. Is it consistent with Ohm's Law?


Can you have an AC series circuit in which there is a phase difference of (a) 180° (b) 120° between the emf and the current?


A resistance is connected to an AC source. If a capacitor is included in the series circuit, will the average power absorbed by the resistance increase or decrease? If an inductor of small inductance is also included in the series circuit, will the average power absorbed increase or decrease further?


Transformers are used ______.


An AC source rated 100 V (rms) supplies a current of 10 A (rms) to a circuit. The average power delivered by the source
(a) must be 1000 W
(b) may be 1000 W
(c) may be greater than 1000 W
(d) may be less than 1000 W


The current in a discharging LR circuit is given by i = i0 et , where τ is the time constant of the circuit. Calculate the rms current for the period = 0 to t = τ.


A coil has a resistance of 10 Ω and an inductance of 0.4 henry. It is connected to an AC source of 6.5 V, `30/pi Hz`. Find the average power consumed in the circuit.


An electric bulb is designed to consume 55 W when operated at 110 volts. It is connected to a 220 V, 50 Hz line through a choke coil in series. What should be the inductance of the coil for which the bulb gets correct voltage?


In a series LCR circuit with an AC source, R = 300 Ω, C = 20 μF, L = 1.0 henry, εrms = 50 V and ν = 50/π Hz. Find (a) the rms current in the circuit and (b) the rms potential difference across the capacitor, the resistor and the inductor. Note that the sum of the rms potential differences across the three elements is greater than the rms voltage of the source.


Consider the situation of the previous problem. Find the average electric field energy stored in the capacitor and the average magnetic field energy stored in the coil.


What is the value of power factor for a pure resistor connected to an alternating current source ? 


What is the net power absorbed by each circuit over a complete cycle. Explain your answer.


At a hydroelectric power plant, the water pressure head is at a height of 300 m and the water flow available is 100 m3 s–1. If the turbine generator efficiency is 60%, estimate the electric power available from the plant (g = 9.8 ms–2).


Power factor of the A. C. circuit varies between ______.

The power factor of series LCR circuit when at resistance is


The average power dissipation in a pure capacitor in A.C circuit is


Which of the following quantities remains constant in a step-down Transformer?


The power factor of an a.c circuit having resistance R and inductance L Connected in series to an a.c source of angular frequency co is.


The series combination of R, L, C is connected to an a.c. source. If the resistance is 3 and the reactance is 4, the power factor of the circuit is:


In an AC. circuit, the current is :

i = `5 sin (100t - pi/2)` amp.

and the a.c. potentiol is:

V = 200 sin (100t) volt.

Then the power consumption is


A 100 Ω electric iron is connected to 200 V, 50 Hz ac source. Calculate average power delivered to iron, peak power and energy spent in one minute?


In the series LCR circuit, the power dissipation is through ______


The coefficient of induction of a choke coil is 0.1 H and resistance is 12 Ω. If it is connected to an a.c source of frequency 60Hz. Then the power factor will be ______.


Share
Notifications



      Forgot password?
Use app×