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MHT-CET : Physics Entrance Exam

MHT - CET : Physics - Electomagnetic Induction Page 6

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14. Inductance and Capacitance

 

(i) A.C. applied to an inductance L:


Let the a.c. current in the coil be

I = I0 sin wt. By Faraday's law e = L  

dI

dt


\ e = wLI0 cos wt

\ e = e0 sin (wt + p / 2 ) where e0 = wLI0.

Thus the a.c. voltage leads the a.c. current by 90.

Also, 

e0

 = wL

I0

 

The ratio of peak voltage to peak current is the reactance offered by the inductance. 

 

(just as 

V

  = R in a conductor ).

I


\ XL = wL = 2p fL


(ii) A.C. applied to a capacitor C:


Let the voltage across the capacitor be ec .
e = ec = e0 sin wt

q = C.ec ( c = q/
v)

I =

dq

=

d

 (C ec) =c 

d

 (eo sinwt)

dt

dt

dt


\ I = wce0 cos wt

\ I = I0 sin (wt + p/2 ) where I0 = e0c w.

Thus the a.c. current leads the a.c. voltage by 90.

Also,  

e0

=

1

I0

wC

 

\ Xc =    

1

=

1

wC

2pfC

 

 

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