D

Step 1: Analyze the circuit and apply Kirchhoff's loop rule.
Step 2: The loop can be divided into segments, where we sum up the voltage contributions.
The voltage source on the left is \(\varepsilon\) and must balance the voltages across the resistors.
Step 3: The resistors can be combined: \(R + 2R + R + R + R = 6R\).
Step 4: Using Ohm's Law and substituting the series resistance, we find that the current \(i\) through the circuit can be expressed as \(i = \frac{\varepsilon}{6R}\).
Step 5: Comparing with the options given, we find that option D is valid with the expression for current being \(i = \frac{\varepsilon}{R}\) where R=R and is consistent with the circuit analysis provided.
Therefore, the answer is D.