Question

A current of $4\text{A}$ flows in a coil when connected to a $12\text{V DC}$ source. If the same coil is connected to a $12\text{V,50 rad/sec}$ AC source a current of $2.4\text{A}$ flows in the circuit choose the correct options.

• A. The inductance of the coil is $0.08\text{Henry}.$
• B. The power developed in the circuit, if a $2500\mu \text{F}$ capacitor is connected in series with the coil is $17.33\text{W}.$
• C. The inductance of the coil is $0.4\text{Henry}.$
• D. The power developed in the circuit, if a $2500\mu \text{F}$ capacitor is connected in series with the coil is $25.28\text{W}.$

Answer 1

Answer: (A), (B)

The correct options are
A The inductance of the coil is $0.08\text{Henry}.$
B The power developed in the circuit, if a $2500\mu \text{F}$ capacitor is connected in series with the coil is $17.33\text{W}.$

$R=\frac{12}{4}\Omega =3\Omega whenconnectedinACcircuiti=\frac{V}{\sqrt{R^2+{\left(\omega L\right)}^2}}=\frac{12}{\sqrt{3^2+{\left(50L\right)}^2}}=2.4\Rightarrow L=0.08Hi=\frac{V}{\sqrt{R^2+{(\frac{1}{\omega C}-\omega L)}^2}}=\frac{12}{\sqrt{3^2+{(\frac{1}{50\times .0025}-50\times 0.08)}^2}}=2.4Atan\phi =\frac{\frac{1}{\omega C}-\omega L}{R}=\frac{4}{3}P=Vicos\phi =12\times 2.4\times \frac{3}{5}=17.28Watt$