An alternating emf is applied across a parallel combination of a resistance R, capacitance C and an inductance L. If `underset(R )(I)`, `underset(L)(I)` and `underset(C )(I)` are the currents through R,L and C respectively, the phase relationship among `underset(R )(I)`, `underset(L)(I)` and `underset(C )(I)` and source emf E, is given by

Options

A.
B.
C.
D.

Explanation

To solve the problem of the phase relationship among the currents through the resistor (IR), inductor (IL), and capacitor (IC) in a parallel AC circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Circuit Configuration**:
- We have a parallel combination of a resistor (R), inductor (L), and capacitor (C) connected to an alternating EMF (E).
- In a parallel circuit, the voltage across all components is the same, which is equal to the source EMF (E).

2. **Identify the Current Relationships**:
- The current through the resistor (IR) is in phase with the EMF (E). This means that the phasor for IR is aligned with the phasor for E.
- The current through the capacitor (IC) leads the voltage across it (E) by 90 degrees (or π/2 radians).
- The current through the inductor (IL) lags the voltage across it (E) by 90 degrees (or π/2 radians).

3. **Draw the Phasor Diagram**:
- Start by drawing the phasor for the EMF (E) along the horizontal axis (real axis).
- Draw the phasor for the current through the resistor (IR) along the same direction as E since they are in phase.
- Draw the phasor for the current through the capacitor (IC) vertically upwards (positive y-axis) because it leads the EMF by π/2.
- Draw the phasor for the current through the inductor (IL) vertically downwards (negative y-axis) because it lags the EMF by π/2.

4. **Analyze the Phasor Relationships**:
- From the phasor diagram, we can see that:
- IR is along the same direction as E.
- IC is along the positive y-axis.
- IL is along the negative y-axis.
- This indicates the phase relationships:
- IR (in phase with E)
- IC (leads E by π/2)
- IL (lags E by π/2)

5. **Select the Correct Option**:
- Based on the analysis and the phasor diagram, we can conclude that the correct option representing the phase relationship among IR, IL, IC, and E is the one that matches our findings.

### Final Answer:
The correct option for the phase relationship among IR, IL, IC, and the source EMF E is **Option C**.