A resistor of 30 Ω, an inductor of inductive reactance 10 Ω and a capacitor of capacitive reactance 10 Ω are connected in series with an a.c. voltage source V = 300√2 sin(ω t) V. The current in the circuit will be .

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(4) 10 A. Given: R = 30 Ω, X_L = 10 Ω, X_C = 10 Ω, peak voltage V₀ = 300√2 V. Idea: in series the reactances subtract, Z = √R² + (X_L - X_C)². X_L - X_C = 0, so Z = R = 30 Ω (the circuit is at resonance). Vᵣₘₛ = (300√2)/(√2) = 300 V, so Iᵣₘₛ = (300)/(30) = 10 A (peak value 10√2 A). The current in the circuit, as an a.c. ammeter shows it, is 10 A.

A resistor of 30 Ω, an inductor of inductive reactance 10 Ω and a capacitor of capacitive reactance 10 Ω are connected in series with an a.c. voltage source V = 300√2 sin(ω t) V. The current in the circuit will be ______.

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