Q.

An inductor and a capacitor are connected in series and altering source V=1202cos100πt 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

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answer is 3.

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Detailed Solution

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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An inductor and a capacitor are connected in series and altering source V=1202cos100πt 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