Question

A parallel combination of an inductor coil and a resistance of $60\Omega$ is connected to an ac source. The current in the coil, current in the resistance and the source current are $3A,2.5A$ and $4.5A$ respectively. Therefore

• A. kirchhoff's current law is NOT applicable to ac circuits
• B. impedance of the coil is $50\Omega$
• C. electric power dissipated in the coil is $150W$
• D. impedance of the circuit is $33.3\Omega$

Answer 1

Answer: (B), (D)

The correct options are
B impedance of the coil is $50\Omega$
D impedance of the circuit is $33.3\Omega$


Rms voltage across resistance$V_{R_{rms}}\Rightarrow 60\times 2.5=150V$
Rms voltage of the ac supply
$V_{rms}=V_{R_{rms}}=150\text{V}$
Impedance
$Z=\frac{V_{rms}}{i_{rms}}\Rightarrow \frac{150}{4.5}=\frac{100}{3}=33.3\Omega \therefore \text{Ans (d)}$
Rms voltage across the coil$V_{L_{rms}}=150=i_{rms}\times X_L=3\times X_L$
$X_L=\frac{150}{3}=50\Omega \therefore \text{Ans. (b)}$
Power dissipated through the inductor$=V_{L_{rms}}{i}_{rms}Cos{90}^{\circ }=0W$
Kirchoffs current law is applicable to AC circuits on an instant by instant basis. It will not be satisfied with averaged rms values.
So correct option are (b) and (d).