Answer
The correct answer is:
(d) The voltage across the resistor is $\varepsilon$.
Work Step by Step
Just after the switch is closed, the voltage across the capacitor is zero. Since the sum of the potential differences across the circuit elements must add to zero, the potential difference across the resistor is $\varepsilon$.
The correct answer is:
(d) The voltage across the resistor is $\varepsilon$.