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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