An inductor and a capacitor are connected in series and altering source $$V=1202cos100$$$$π$$t volt is connected across the combination. The rms current in the circuit is found to be $$5$$ A. When a resistor of resistance R is connected in series with the inductor and capacitor and the same alternating source is used, the rms current in the circuit is found to be $$4$$ A, Then the value of R is

Question

An inductor and a capacitor are connected in series and altering source $$V=1202cos100$$$$π$$t volt  is connected across the combination. The rms current in the circuit is found to be $$5$$ A. When a resistor of resistance R is connected in series with the inductor and capacitor and the same alternating source is used, the rms current in the circuit is found to be $$4$$ A, Then the value of R is

Infinity Learn · Accepted Answer

Let $$I1$$ and v be rms values of current and voltge of LC AC $$circuitI1=vz1=vXL$$−XC⇒XL−$$XC=vI1I2=vz2=vR2+XL$$−$$XC2$$⇒$$R2=v2I22$$−XL−$$XC2=v2I22$$−$$v2I12$$∴$$R=vI12-I22I1I2=120$$×$$52$$−$$425$$×$$4$$Ω$$=18$$Ω

Phasors and Phasor Diagrams

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Phasors and Phasor Diagrams

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Let I1 and v be rms values of current and voltge of LC AC circuitI1=vz1=vXL−XC⇒XL−XC=vI1I2=vz2=vR2+XL−XC2⇒R2=v2I22−XL−XC2=v2I22−v2I12∴R=vI12-I22I1I2=120×52−425×4Ω=18Ω

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