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An alternating voltage with frequency omega=314s^(-1) and amplitude V_(m)=180 V is fed to a series circuit consisting of a capacitor and a coil with active resistor's capacitance will the voltageamplitude across the coil be maximum ? What is this amplitude equal to ? What is the corresponding voltage amplitude across the condenser ? |
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Answer» Solution :`V_(L)= I_(m) sqrt(R^(2) + omega^(2) L^(2))` `= ( V_(m) sqrt(R^(2)+ omega^(2) L^(2)))/( sqrt( R^(2) +(omegaL-(1)/( OMEGAC))^(2)))` for a given `omega , L, R`,this is MAXIMUM when `(1)/( omega C)= omegaL` or `C=(1)/( omega^(2) L ) = 28 . 2 mu F. ` For that `C, ` `V_(L)= (Vsqrt(R^(2)+ omegaL^(2)))/( R) = Vsqrt( 1+ ( omegaL // R )^(2))= 0.540 k V` At this `C` `V_(C)=(1)/(omegaC) (V_(m))/( R)=(V_(m) omega L)/( R)=. 509 k V` |
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