The problem in the image asks for the maximum current flowing through the AC circuit when the maximum voltage of the AC source is $V_{\text{max}} = 200 \, \text{V}$. The circuit includes a resistor (R), an inductor (L), and a capacitor (C) in series with values:

• $R = 60 \, \Omega$
• $X_L = 120 \, \Omega$ (inductive reactance)
• $X_C = 40 \, \Omega$ (capacitive reactance)

Steps to solve:

1. Calculate total impedance (Z): The total impedance for an RLC series circuit is given by: $Z = \sqrt{R^2 + (X_L - X_C)^2}$ Substituting the given values: $Z = \sqrt{60^2 + (120 - 40)^2} = \sqrt{60^2 + 80^2} = \sqrt{3600 + 6400} = \sqrt{10000} = 100 \, \Omega$

2. Maximum current (Imax): The maximum current in an AC circuit is given by Ohm's law: $I_{\text{max}} = \frac{V_{\text{max}}}{Z}$ Substituting the values: $I_{\text{max}} = \frac{200 \, \text{V}}{100 \, \Omega} = 2.0 \, \text{A}$

Thus, the maximum current that flows through the circuit is 2.0 A, corresponding to option (d).

Would you like further details or have any questions about this solution?

Here are some related questions to explore:

1. How do we calculate inductive and capacitive reactances?
2. What is the effect of increasing the inductance on the current in this circuit?
3. How would the phase angle between the current and voltage change if the inductive reactance increased?
4. Can you explain the physical meaning of impedance in an AC circuit?
5. How does the resonance condition affect the current in an RLC circuit?

Tip: In AC circuits, the impedance acts like resistance in DC circuits but also considers the phase shift between voltage and current due to inductors and capacitors.