The phase diffenernce between the alternating current and emf is `(pi)/(2)`. Which of the following cannot be the constiuent of the circuit?

Options

A. R,L
B. C alone
C. L alone
D. L,C

Explanation

To solve the problem, we need to analyze the phase difference between the alternating current (AC) and the electromotive force (emf) in different circuit configurations. The phase difference given is \( \frac{\pi}{2} \) radians. We will evaluate each option to determine which component cannot exist in such a circuit.

### Step-by-Step Solution:

1. **Understanding Phase Difference**:
- The phase difference between AC and emf is \( \frac{\pi}{2} \). This indicates that the current leads or lags the voltage by 90 degrees.

2. **Analyzing Each Option**:
- We will evaluate each of the four options to see if they can produce a phase difference of \( \frac{\pi}{2} \).

3. **Option 1: Resistance (R) and Inductor (L)**:
- In a circuit with both resistance and inductance, the phase difference \( \phi \) can be calculated using:
\[ \tan(\phi) = \frac{X_L}{R} \]
where \( X_L \) is the inductive reactance. The phase difference can range from \( 0 \) to \( \frac{\pi}{2} \) but cannot be exactly \( \frac{\pi}{2} \) because that would imply infinite resistance (which is not possible). Therefore, this configuration cannot have a phase difference of \( \frac{\pi}{2} \).

4. **Option 2: Pure Capacitive Circuit (C)**:
- In a pure capacitive circuit, the phase difference is \( -\frac{\pi}{2} \) (current leads voltage). This means that while it does not match \( \frac{\pi}{2} \), it is still a valid phase difference. Thus, this option is possible.

5. **Option 3: Pure Inductive Circuit (L)**:
- In a pure inductive circuit, the phase difference is \( \frac{\pi}{2} \) (current lags voltage). This matches our requirement exactly, so this option is also possible.

6. **Option 4: Inductor (L) and Capacitor (C)**:
- In a circuit with both inductance and capacitance, the phase difference can vary widely depending on the values of L and C. It can take values from \( 0 \) to \( \frac{\pi}{2} \) and beyond. Therefore, this option can also achieve a phase difference of \( \frac{\pi}{2} \).

### Conclusion:
The only option that cannot have a phase difference of \( \frac{\pi}{2} \) is **Option 1: Resistance (R) and Inductor (L)**.