A

When switch S is opened in the given circuit, we can analyze the effects step-by-step:
Step 1: Equivalent resistance across the battery
When the switch S is closed, the total equivalent resistance is determined by both resistors in parallel (if they are configured as such). Opening the switch does not add or remove any resistors; it only opens the path of current through the left resistor. Therefore, the equivalent resistance across the battery remains the same.
Step 2: Power dissipated by left resistance R
The power dissipated is given by the formula P = I^2R. When the switch is opened, the current through the left resistance R becomes zero. As a result, the power dissipated by the left resistance also becomes zero. Thus, the power does not increase; instead, it decreases.
Step 3: Voltmeter reading
A voltmeter reads the potential difference across a component. If there is no current flowing through the left resistor when the switch is opened, the voltmeter connected across the left resistor will read zero. Therefore, the voltmeter reading decreases.
Step 4: Ammeter reading
Since the current in the circuit is interrupted when the switch is opened, the reading on the ammeter becomes zero because there is no flow of current through the circuit.
By matching the parameters:

• (i) Equivalent resistance -> [A] Remains same
• (ii) Power dissipated by left resistance R -> [B] Increases (this is incorrect as it decreases)
• (iii) Voltmeter reading -> [C] Decreases
• (iv) Ammeter reading -> [D] Becomes zero

Hence, the correct matching is (i) [A], (ii) [B], (iii) [C], (iv) [D]. Therefore, option A, regarding the equivalent resistance, remains the same.