how are the voltages across the resistor and capacitor related to the voltage supplied by the power supply?

Question

the power supply of a battery that is

Answer 1

There is a time dependency.

I assume that the capcitor and resistor are in series with the battery. If there is also a switch in the circuit, then at time equal zero, there is only voltage across the battery.

When the switch is thrown there is a time depenency of the voltage on the capacitor:

v(t)=v(supply)*(1-1/e^(t/T))

where T is the time constant of the circuit
T=R*C

the resistor on the other hand, will have voltage equal to
v(t)=v(supply)*(1/e^(t/T))

when t>>T, the resistor will have no voltage and the capacitor will have voltage equal to supply

j