Question

A $90\Omega$ resistor, a coil with $30\Omega$ of reactance, and a capacitor with $50\Omega$ of reactance are in series across a $12V$ ac source. The current through the resistor is

• A. $9mA$
  
• B. $90mA$
  
• C. $13mA$
  
• D. $130mA$
  

Answer 1

The correct option is D $130mA$

Resistance=$R=90\Omega$

Reactance of coil$=X_L=30\Omega$

Reactance of capacitor$=X_C=50\Omega$

Impedance of circuit$=X=\sqrt{R^2+(X_C-X_L{)}^2}$

$⟹X=\sqrt{{90}^2+(50-30{)}^2}=\sqrt{8100+400}$

Current$=I=\frac{E}{X}=\frac{12}{\sqrt{8500}}$

$⟹I=0.13A=130mA$

Answer-(D)