The given circuit is an RLC series circuit powered by an AC voltage source $V_s(t) = 800 \angle -25^\circ$ volts, where we have a resistor $R$, an inductor $L$, and a capacitor $C$ in series.

Here’s how we can analyze the circuit to find the current:

Step 1: Convert the Voltage Source to Phasor Form

The voltage source is already given in phasor form: $V_s = 800 \angle -25^\circ \text{ volts}.$

Step 2: Impedance Calculation

We need to calculate the impedances of the resistor, inductor, and capacitor at a given frequency $\omega$.

1. Resistor Impedance: The impedance of a resistor is purely real and is simply $R$. $Z_R = R.$ From the image, the value of $R$ isn't explicitly given, but $v_R = 30$ V suggests we will need this information to find the current.

2. Inductor Impedance: The impedance of an inductor is given by: $Z_L = j \omega L.$ Where $\omega$ is the angular frequency of the source (we will need the source frequency for further calculation).

3. Capacitor Impedance: The impedance of a capacitor is given by: $Z_C = \frac{1}{j \omega C}.$ Again, this depends on the angular frequency $\omega$.

Step 3: Total Impedance of the Circuit

The total impedance $Z_{\text{total}}$ is the sum of the impedances of the resistor, inductor, and capacitor: $Z_{\text{total}} = Z_R + Z_L + Z_C = R + j \omega L + \frac{1}{j \omega C}.$

Step 4: Finding the Current

Once we have the total impedance, the current in the circuit can be calculated using Ohm's Law in phasor form: $I_s = \frac{V_s}{Z_{\text{total}}}.$

To complete the calculation, we would need either the frequency $f$ or the angular frequency $\omega$ of the source. Could you provide the frequency or clarify the value of $R$?

Here are five related questions you might consider:

1. What is the angular frequency or the frequency of the voltage source $V_s(t)$?
2. Is the value of the resistor $R$ given elsewhere in the problem or in other parts of the circuit?
3. Should we assume a standard frequency (like 60 Hz or 50 Hz) for the AC source?
4. Would you like a step-by-step explanation of how to derive the impedance of inductors and capacitors in AC circuits?
5. How do phase angles affect current calculations in an RLC circuit?

Tip: When solving AC circuits, always make sure to work in phasor form for both voltage and current, as this simplifies the handling of sinusoidal sources.