A series LCR circuit consists of $$R = 80$$ $$\Omega$$. $$X_L = 100$$ $$\Omega$$, and $$X_C = 40$$ $$\Omega$$. The input voltage is 2500 $$\cos(100\pi t)$$ V. The amplitude of current, in the circuit, is ______ A.

We are given a series LCR circuit with $$R = 80$$ $$\Omega$$, $$X_L = 100$$ $$\Omega$$, $$X_C = 40$$ $$\Omega$$, and input voltage $$V = 2500\cos(100\pi t)$$ V.

$$ Z = \sqrt{R^2 + (X_L - X_C)^2} $$

$$ Z = \sqrt{80^2 + (100 - 40)^2} = \sqrt{6400 + 3600} = \sqrt{10000} = 100 \text{ } \Omega $$

From $$V = 2500\cos(100\pi t)$$, the amplitude (peak voltage) is $$V_0 = 2500$$ V.

$$ I_0 = \frac{V_0}{Z} = \frac{2500}{100} = 25 \text{ A} $$

The amplitude of current in the circuit is 25 A.