Question 438: AC fundamentals

Question

To an ac power supply of 220 V at 50 Hz , a resistor of $20 \Omega$, a capacitor of reactance $25 \Omega$ and an inductor of reactance $45 \Omega$ are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively

Accepted Answer

To determine the current in the circuit and the phase angle between the current and voltage, follow these steps:
Components and their Reactance:
Inductive reactance, $ X_L = 45 \, \Omega $
Capacitive reactance, $ X_C = 25 \, \Omega $
Resistance, $ R = 20 \, \Omega $
Calculate Current (I):
The current through the series circuit can be calculated using the formula:
$    I = \frac{V}{\sqrt{(X_L - X_C)^2 + R^2}}    $
Substituting the given values:
$    I = \frac{220}{\sqrt{(45 - 25)^2 + 20^2}} = \frac{220}{\sqrt{20^2 + 20^2}}    $
Simplifying further:
$    I = \frac{220}{\sqrt{400 + 400}} = \frac{220}{\sqrt{800}} = \frac{220}{2\sqrt{200}} = \frac{220}{2\sqrt{100 	imes 2}} = \frac{220}{20\sqrt{2}} = \frac{11}{\sqrt{2}}     $
Therefore, the current is approximately:
$    I = 7.779 \, 	ext{A} \, (\approx 7.8 \, 	ext{A})    $
Calculate Phase Angle ($\phi$):
The phase angle can be calculated using the tangent of the angle:
$    	an \phi = \frac{X_L - X_C}{R} = \frac{45 - 25}{20} = \frac{20}{20} = 1    $
Hence, the phase angle $\phi$ is:
$    \phi = 45^{\circ}    $
Thus, the current in the circuit is approximately 7.8 A, and the phase angle is $45^{\circ}$.

Answer

15.6 A and $30^{\circ}$

Answer

15.6 A and $45^{\circ}$

Answer

7.8 A and $30^{\circ}$

Answer

7.8 A and $45^{\circ}$

AC fundamentals

To an ac power supply of 220 V at 50 Hz , a resistor of 20 \Omega, a capacitor of reactance 25 \Omega and an inductor of reactance 45 \Omega are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively

Choose the correct answer: