A sine voltage having a maximum value of 283 V and frequency 50 Hz is applied to an LCR series connection where R=3 Ω, L=25.48 mH and C=796 μF. Then the impedance is at the resonance condition.

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(1) 3 Ω. Given: R=3 Ω, L=25.48 mH and C=796 μF. Idea: at resonance X_L=X_C, so they cancel and Z=√R²+(X_L-X_C)²=R. So at the resonance condition Z=R=3 Ω. The peak voltage is not needed. Check: resonance occurs at f₀=1/(2π√LC)=1/(2π√25.48×10⁻³×796×10⁻⁶)≈35.4 Hz. At the source's own 50 Hz the circuit is not at resonance: X_L=8 Ω, X_C=4 Ω and Z=5 Ω. So the impedance at the resonance condition is 3 Ω.

A sine voltage having a maximum value of 283 V and frequency 50 Hz is applied to an LCR series connection where R=3 Ω, L=25.48 mH and C=796 μF. Then the impedance is ______ at the resonance condition.

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