Aresistor and a capacitor are connected in series to an ideal battery of constant terminal voltage. when the system reaches its steady state, what is the voltage across the resistor and the capacitor?

the voltage across both the resistor and the capacitor is equal to one-half of the terminal voltage of the battery.
the voltage across the resistor is equal to the terminal voltage of the battery, and the voltage across the capacitor is zero.
the voltage across the resistor is zero, and the voltage across the capacitor is equal to the terminal voltage of the battery.
the voltage across both the resistor and the capacitor is equal to the terminal voltage of the battery.
the voltage across both the resistor and the capacitor is zero

The voltage across the resistor is zero, and the voltage across the capacitor is equal to the terminal voltage of the battery.

Explanation:

In a series circuit, the current is the same for all the components. While the circuit reaches its steady state, the capacitor charges and the voltage across its plates increases until it reaches the one on the terminals, and at that point it is in the steady state.

In the instant the circuit is connected, the voltage across the capacitor would be zero (it doesn't have any charge yet) so by Kirchoff's voltage law all the voltage is in the resistor. But as the capacitor charges, the voltage across its plates increases, which produces a decrease on the voltage across the resistor. This continues until the voltage across the capacitor equals the one on the terminals, which in turn makes the voltage across the resistor zero.

frequency or wavelenth of em radiation in a vacuum