Question

An electric motor when loaded has an effective resistance of $30\,\Omega$ and an inductive reactance of $40\,\Omega$. If the motor is powered by a source with maximum voltage of $420\,V$, the maximum current is

• A. $6$ A
• B. $8.4$ A
• C. $10$ A
• D. $12$ A
• E. $13$ A

Hint:

Always use impedance in AC circuits: $Z=\sqrt{R^2+X^2}$.

Answer 1

The Correct Option is B

Concept:
\[ Z = \sqrt{R^2 + X_L^2}, \quad I_{max} = \frac{V_{max}}{Z} \]

Step 1: Impedance.
\[ Z = \sqrt{30^2 + 40^2} = \sqrt{900 + 1600} = 50\,\Omega \]

Step 2: Current.
\[ I_{max} = \frac{420}{50} = 8.4\,A \]