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MHT-CET : Physics Entrance Exam

MHT - CET : Physics - Electomagnetic Induction Page 5

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11. Rotating Coil in a Uniform Magnetic Field (Alternating e.m.f.)

 

Coil is rotating in a uniform magnetic field. Suppose a coil is rotated with a uniform angular speed w about an axis in its plane, passing through its centre and perpendicular to a uniform magnetic induction .

The flux passing through the coil goes on changing as it rotates.
At time t, number of lines of flux linked with coil is given by
f = NAB cos q = NAB cos w t ( ... q = w t )

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

 

e = - 

df

 = wNAB sin w t = e0 sin wt

dt


\ e = e0sinwt. Where e0 = NABw.

A graph of this equation and a table showing values of e at t =  

T

T

,

3T

 

4

2

4

and T is given below:

t

0

T/4

T/2

3T/4

T

e

0

e0

0

- e0

0



Graph shows variation of induced emf with time "
t".

 

Note:

 

(i) e.m.f. varies continuously
(ii) e.m.f. changes its direction after every half rotation.
Such an e.m.f. is called alternating e.m.f.

 

12.

A.C. Circuits with Resistance only

 


An alternative e.m.f. applied across a resistance

E.m.f. applied: e = e0 sin

wt current in the circuit : I =  

e0 sin wt

R

\ I =

I0sin wt

 

 

where I0 =

e0

.

R


The current and the e.m.f. reach their maximum and minimum values simultaneously, i.e. they are in phase.

Power in A.C. Circuits with Resistance only:

 

Let e = e0 sin wt be the voltage applied to resistance R.

I= 

e

=

e0 sinwt

 = I0 sin wt

R

R

 

The instantaneous power P = e.I = ( e0 sin wt) (i0 sin wt) = 

e02

 sin 2t

R

 

The average power Pav =  

 = erms Irms.

SI unit of Power : watt

 

rms value: Root-mean-square (rms) value of an alternating current / e.m.f. is defined as that value of steady (D.C.) current which when passed through the same resistor for the same interval of time produces the same quantity of heat as the alternating current / e.m.f.

 

 

Irms

I0

 

 

erms

e0

Peak value: Maximum values are called peak values.
When sin wt = 1

 

e= e0 and I = I0 =

e0

.

R

 

13. Reactance and Impedance

 

 

Impedance (Z):

Devices in an electrical circuit offer resistance as well as reactance to the flow of alternative current through them. The combined effect of resistance and reactance is called the impedance (Z) of the circuit.

(impedance)2

= (resistance)2 + (reactance)2

 

Z2 = R2 + (XL ~ Xe)2


The SI unit of impedance is ohm.

 

 

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