Physics - EMI/AC Question with Solution | TestHub

The question asks for the total impedance of a series RLC circuit.

Given:

Resistance $R=30\Omega$

Capacitive reactance $X_C=40\Omega$

Inductive reactance $X_L=80\Omega$

The total impedance $Z$ for a series RLC circuit is given by the formula:

$$Z=\sqrt{R^2+(X_L-X_C{)}^2}$$

Substitute the given values:

$$Z=\sqrt{(30\Omega {)}^2+(80\Omega -40\Omega {)}^2}$$

$$Z=\sqrt{(30\Omega {)}^2+(40\Omega {)}^2}$$

$$Z=\sqrt{900{\Omega }^2+1600{\Omega }^2}$$

$$Z=\sqrt{2500{\Omega }^2}$$

$$Z=50\Omega$$

The total impedance of the circuit is $50\Omega$.

The correct answer is B.