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Alternating Current question

2025 · Q156
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Alternating Current question

2025 · Q156

NEETPhysicsAlternating CurrentMCQ+4 / −1

To an ac power supply of 220 V at 50 Hz , a resistor of 20Ω20 \Omega20Ω, a capacitor of reactance 25Ω25 \Omega25Ω and an inductor of reactance 45Ω45 \Omega45Ω are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively

  1. A
    15.6 A and 30∘30^{\circ}30∘
  2. B
    15.6 A and 45∘45^{\circ}45∘
  3. C
    7.8 A and 30∘30^{\circ}30∘
  4. D
    7.8 A and 45∘45^{\circ}45∘
View written solutionFree

Correct answer: D

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 \times 2}} = \frac{220}{20\sqrt{2}} = \frac{11}{\sqrt{2}} $

Therefore, the current is approximately:

$ I = 7.779 \, \text{A} \, (\approx 7.8 \, \text{A}) $

Calculate Phase Angle ($\phi$):

The phase angle can be calculated using the tangent of the angle:

$ \tan \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 $45^{\circ}$.

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