Question

In the circuit shown, a 30 V d.c source gives a current 2.0A as recorded in the ammeter A and 30V a.c. source of frequency 100Hz gives a current 1.2A. The inductive reactance is

• A. 10ohm
• B. 20 ohm
• C. $5\sqrt{34}$ ohm
• D. 40 ohm

Answer 1

The correct option is B 20 ohm

In DC current

$V=iR$

$\frac{V}{i}=R$

$R=\frac{30}{2}=15\Omega$

In a.c. current

$V=iImpedance$

$\frac{V}{i}=Impedance$

$Impedance=\frac{30}{1.2}=25\omega$

$Impedance=\sqrt{R^2+(X_L{)}^2}$

$(25{)}^2=R^2+(X_L{)}^2$

$X_L=\sqrt{(25{)}^2-R^2}$

$=\sqrt{625-225}$

$=\sqrt{400}$

$=20\Omega$