A voltage V(t) = 220 sin(2 × 10³t) V is applied to a series RLC circuit with L = 10 mH, C = 25 μF and R = 100 Ω. Find the amplitude of the circuit current.
Options

Question

A voltage V(t) = 220 sin(2 × 10³t) V is applied to a series RLC circuit with L = 10 mH, C = 25 μF and R = 100 Ω. Find the amplitude of the circuit current.

G1 Physics · Accepted Answer

Step 1: Angular frequency ω = 2 × 10³ rad s⁻¹ and voltage amplitude V₀ = 220 V. Step 2: Inductive reactance X_L = ωL = (2000)(0.010) = 20 Ω. Step 3: Capacitive reactance X_C = 1/(ωC) = 1/[2000 × 25 × 10⁻⁶] = 20 Ω. Step 4: Reactances cancel at resonance; impedance Z = √[R² + (X_L − X_C)²] = 100 Ω. Step 5: Current amplitude I₀ = V₀/Z = 220/100 = 2.2 A. Final answer: 2.2 A (Option A).