For a series R-L-C circuit :-
(a) Voltage across L and C are differ by `pi`
(b) Current through L and R are in same phase
(c) Voltage across R and L differ by `pi//2`
(d) Voltage across L and current through C are differ by `pi//2`

Options

A. a,b,c
B. b,c,d
C. c,d,a
D. ALL

Answer

To solve the problem regarding the phase relationships in a series R-L-C circuit, let's analyze each of the given options step by step.

### Step 1: Understanding the Phase Relationships
In a series R-L-C circuit:
- The current (I) is the same through all components (R, L, and C).
- The voltage across the resistor (V_R) is in phase with the current.
- The voltage across the inductor (V_L) leads the current by π/2 (90 degrees).
- The voltage across the capacitor (V_C) lags the current by π/2 (90 degrees).

### Step 2: Analyzing Each Option
Now, let's analyze each of the options provided in the question:

#### Option (a): Voltage across L and C differ by π
- The voltage across the inductor (V_L) leads the current by π/2, and the voltage across the capacitor (V_C) lags the current by π/2.
- Therefore, the phase difference between V_L and V_C is π (180 degrees).
- **Conclusion**: This statement is **correct**.

#### Option (b): Current through L and R are in the same phase
- Since the circuit is in series, the current through the inductor (I_L) and the current through the resistor (I_R) are the same.
- **Conclusion**: This statement is **correct**.

#### Option (c): Voltage across R and L differ by π/2
- The voltage across the resistor (V_R) is in phase with the current, while the voltage across the inductor (V_L) leads the current by π/2.
- Therefore, the phase difference between V_R and V_L is π/2.
- **Conclusion**: This statement is **correct**.

#### Option (d): Voltage across L and current through C differ by π/2
- The voltage across the inductor (V_L) leads the current by π/2, while the current through the capacitor (I_C) lags the voltage across the capacitor (V_C) by π/2.
- Since V_L leads the current and I_C lags the voltage, the phase difference between V_L and I_C is indeed π/2.
- **Conclusion**: This statement is **correct**.

### Final Conclusion
All four options are correct. Therefore, the answer is that all statements (a, b, c, d) are true.