Final answer:
The voltage across a resistor immediately after a switch is closed in a DC circuit will typically be equal to the source voltage. This voltage can vary in circuits with capacitors and inductors. For an open switch, the voltage across it equals the source voltage as there's no current flow.
Step-by-step explanation:
The question you asked pertains to the behavior of electric circuits when switches are engaged or disengaged. When a switch is closed in an electric circuit that includes a resistor, the voltage across the resistor immediately after closing the switch depends on the circuit configuration. If the resistor is in series with a battery or voltage source and the switch, the voltage across the resistor will ideally equal the voltage of the source immediately after closing the switch, as no current has yet flowed through any potential capacitors to change this condition.
However, for circuits containing capacitors or inductors, the situation can be different due to the time-dependent nature of current and voltage in those elements. In a DC circuit with a capacitor, the voltage across the capacitor, and therefore across the resistor in parallel with it, starts at zero and increases as the capacitor charges over time. For inductive circuits, the behavior depends on the inductance and the resistance in the circuit. It is essential to have a complete circuit diagram to provide a definitive answer.
Regarding your reference to an open switch, the voltage across an open switch is usually equal to the voltage of the source because there is no current flow through the open switch, thus no voltage drop across any other circuit elements.