In series LCR AC circuit, the voltage of the source at any instant is equal to

Options

A. The sum of the maximum voltage across the elements
B. The voltage drop across the resistor
C. The sum of the instantaneous voltages across the elements
D. The sum of the rms voltages across the elements

Answer

To find the voltage of the source at any instant in a series LCR AC circuit, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understand the Circuit Components**:
- In a series LCR circuit, we have three main components: an inductor (L), a capacitor (C), and a resistor (R). The circuit is powered by an alternating current (AC) voltage source.

2. **Identify the Instantaneous Voltages**:
- The instantaneous voltages across each component can be represented as:
- Voltage across the resistor (V_R)
- Voltage across the inductor (V_L)
- Voltage across the capacitor (V_C)

3. **Apply Kirchhoff's Voltage Law**:
- According to Kirchhoff's Voltage Law, the sum of the instantaneous voltages across all elements in a closed loop is equal to the instantaneous voltage of the source (V_s). Therefore, we can write:
\[ V_s = V_R + V_L + V_C \]

4. **Conclusion**:
- From the above equation, we can conclude that the voltage of the source at any instant is equal to the sum of the instantaneous voltages across the resistor, inductor, and capacitor. Thus, the correct answer is:
\[ V_s = V_R + V_L + V_C \]

### Final Answer:
The voltage of the source at any instant in a series LCR AC circuit is equal to the sum of the instantaneous voltages across the elements.

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