Statement 1: In the purely resistive element of a series LCR, ac circuit the maximum value of rms current increase with increase in the angular frequency of the applied emf.
Statement 2: `I_(max)=(epsilon_(max))/(Z), Z=sqrt(R^(2)+(omega L-(1)/(omega C)^(2)))`,
where `(I_(max))` is the peak current in a cycle.

Options

A. Statement 1 is true, statement 2 is true, Statement 2 is the correct explanation for statement 1.
B. Statemet 1 is True, Statement 2 is true , Statement 2 is NOT the correct explanation for Statement 1
C. Statement 1 is True, Statement 2 is False.
D. Statement 1 is False, Statement 2 is true

Explanation

To analyze the given statements, we need to understand the behavior of a series LCR circuit under alternating current (AC) conditions. Let's break down the statements and derive the necessary conclusions step by step.

### Step 1: Understanding the Circuit
In a series LCR circuit, we have a resistor (R), an inductor (L), and a capacitor (C) connected in series. The total impedance (Z) of the circuit is given by:
\[ Z = \sqrt{R^2 + \left( \omega L - \frac{1}{\omega C} \right)^2} \]
where:
- \( \omega \) is the angular frequency of the applied EMF.

### Step 2: Analyzing Statement 1
**Statement 1:** "In the purely resistive element of a series LCR circuit, the maximum value of the RMS current increases with an increase in the angular frequency of the applied EMF."

- In a purely resistive circuit, the impedance \( Z \) is simply \( R \).
- The maximum current \( I_{\text{max}} \) can be expressed as:
\[ I_{\text{max}} = \frac{E_{\text{max}}}{Z} \]
- As the frequency increases, the reactive components (inductive and capacitive) do not contribute to the impedance in a purely resistive circuit. Therefore, the impedance remains constant at \( R \).
- Thus, the maximum current does not increase with frequency; it remains constant.

**Conclusion for Statement 1:** This statement is **false**.

### Step 3: Analyzing Statement 2
**Statement 2:** "I_{\text{max}} = \frac{E_{\text{max}}}{Z}, Z = \sqrt{R^2 + \left( \omega L - \frac{1}{\omega C} \right)^2}."

- This equation is indeed correct for a series LCR circuit.
- The expression for impedance \( Z \) is accurate and reflects the total opposition to current flow in the circuit.
- However, the statement does not directly address the behavior of current with respect to frequency in a purely resistive circuit.

**Conclusion for Statement 2:** The statement is **true** in terms of the formula provided, but it does not apply to the context of purely resistive elements as described in Statement 1.

### Final Conclusion
- **Statement 1:** False
- **Statement 2:** True