A series R-C circuit is connected to an AC voltage source. Consider two cases: (A) when C is without a dielectric medium and (B) when C is filled with a dielectric of constant 4. The current IR through the resistor and voltage VC across the capacitor are compared in the two cases. Which of the following is/are true?

The impedance of a series R-C circuit is given by Z = √(R² + (1/ωC)²), where R is the resistance, ω is the angular frequency of the AC source, and C is the capacitance. The current I is given by I = V/Z, where V is the voltage of the AC source.

Case A: Without dielectric, the capacitance is C.
Case B: With dielectric constant 4, the capacitance becomes 4C.

Let's analyze the current through the resistor (IR) in both cases:

Case A: IA = V/√(R² + (1/ωC)²)
Case B: IB = V/√(R² + (1/(4ωC))²)

Since the denominator in Case B is smaller than in Case A (because 1/(4ωC) < 1/ωC), IB > IA. Therefore, IAR < IBR is true.

Now let's analyze the voltage across the capacitor (VC):

VC = I * (1/ωC)

Case A: VAC = [V/√(R² + (1/ωC)²)] * (1/ωC)
Case B: VBC = [V/√(R² + (1/(4ωC))²)] * (1/(4ωC))

Comparing VAC and VBC is not straightforward from these equations. However, since IB > IA and the term (1/ωC) in Case B is smaller than that in Case A, it's not immediately obvious whether VAC > VBC or VAC < VBC. A more detailed analysis considering the relative magnitudes of R and 1/ωC would be necessary to definitively determine the relationship between VAC and VBC. However, the relationship between the currents is clearly established.