To solve the problem, we will analyze the relationships between the instantaneous voltages in a series L-C-R circuit connected to a variable frequency source of emf.
### Step-by-Step Solution:
1. **Understanding the Circuit**:
In a series L-C-R circuit, the voltages across the inductor (V_L), capacitor (V_C), and resistor (V_R) are related to the total voltage (V) across the circuit. The relationships can be expressed in terms of phasors.
2. **Voltage Relationships**:
- The voltage across the resistor (V_R) is in phase with the current.
- The voltage across the inductor (V_L) leads the current by \( \frac{\pi}{2} \) (90 degrees).
- The voltage across the capacitor (V_C) lags the current by \( \frac{\pi}{2} \) (90 degrees).
3. **Phasor Diagram**:
When we draw the phasor diagram, we can represent:
- V_R along the horizontal axis.
- V_L vertically upwards (since it leads).
- V_C vertically downwards (since it lags).
4. **Total Voltage (V)**:
The total voltage \( V \) can be represented as:
\[
V = V_R + (V_L - V_C)
\]
This means that \( V \) can be expressed in terms of the voltages across the inductor and capacitor.
5. **Analyzing Each Option**:
- **(A) |V|**: The magnitude of the total voltage can be greater than zero (P is correct).
- **(B) |V| - |V_L|**: This can be greater than zero, less than zero, or equal to zero depending on the values of V and V_L (P, Q, R are correct).
- **(C) |V| - |V_C|**: Similar to option B, this can also be greater than zero, less than zero, or equal to zero (P, Q, R are correct).
- **(D) |V| - |V_R|**: The total voltage can be greater than or equal to V_R, but it cannot be less than zero (P and R are correct).
6. **Final Answers**:
- For (A): P (can be greater than zero)
- For (B): P, Q, R (can be greater than, less than, or equal to zero)
- For (C): P, Q, R (can be greater than, less than, or equal to zero)
- For (D): P, R (can be greater than or equal to zero)
### Summary of Correct Options:
- (A) P
- (B) P, Q, R
- (C) P, Q, R
- (D) P, R
