A 2.2 nF capacitor and a capacitor of unknown capacitance areconnected in parall

Question

A 2.2 nF capacitor and a capacitor of unknown capacitance areconnected in parallel across a 12 V rms sine-wave generator. At 1.0kHz, the generator supplies a total current of 3.4 mA rms. Thegenerator frequency is then decreased until the rms current hasdropped to 1.1 mA. Find (a) the unknown capacitance                Answer:__________________ nF (b) the lower frequency.
               Answer:____________ Hz A 2.2 nF capacitor and a capacitor of unknown capacitance areconnected in parallel across a 12 V rms sine-wave generator. At 1.0kHz, the generator supplies a total current of 3.4 mA rms. Thegenerator frequency is then decreased until the rms current hasdropped to 1.1 mA. Find (a) the unknown capacitance                Answer:__________________ nF (b) the lower frequency.
               Answer:____________ Hz

Explanation / Answer

   Let the unknown capacitancebe   C   nF   , Thenequivalent capacitance of circuit    Ceq   =   (C+2.2)   nF      -----------(1)    a.   Current incircuit   Irms   =   Vrms/ XC    XC   =   12/ 3.4 * 10-3   =   3.53 *103       Also   XC   =   1/ * Ceq   =   1/ 2 * * f * Ceq    Ceq   =  1/ 3.53* 103 *2 * 3.14 *1000   =   4.51 *10-8   F   =   45.1   nF    From equation(1)   C   =   Ceq   -   2.2   =   45.1   -   2.2   =   42.9   nF    b.      Letthe lower frequency be    F, then       Xc   =   Vrms/ Irms   =   12 / 1.1 *10-3   =   1.09 *104          1 / ' *Ceq   =   1.09 *104    '   =   2 * * F   =   1 / 1.09 *104 * 45.1 * 10-9       F   =   1/ 1.09 * 104 * 45.1 * 10-9 *6.28   =   3.239 *102   =   323.9   Hz   ˜   324   Hz       F   =   1/ 1.09 * 104 * 45.1 * 10-9 *6.28   =   3.239 *102   =   323.9   Hz   ˜   324   Hz

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