Energy stored in a capacitor Suppose we  have a capacitor connected in series with a resistor and this is connected to a cell. So would the voltage across the capacitor be less than the the emf of the cell? And hence the energy stored? Because of the potential drop across the resistor?
 A: 
Here, initially some current flows through R1 and C1 but only until C1 gets fully charged once C1 is fully charged no current flows through the resistor.
If you charge up a capacitor through a resistor current will flow until the voltage across the capacitor is the same as the source. This is an exponential process and never really gets there but it comes pretty close after some time.
When this happens current doesn't flow through the resistor That means the voltage drop across the capacitor is equal to the EMF of the cell.
Energy stored in a capacitor would be = 1/2*QV or 1/2*C*V^2. (V is now the EMF of battery, C is the capacitance of the capacitor, Q is the charge on the capacitor.)
A: When the capacitor is fully charged, there is no current flowing through the resistor. From Ohms law, the voltage drop across the resistor is zero. That means the voltage drop across the capacitor is equal to the EMF of the cell. You can then find the energy in the capacitor.
A: The resistor/capacitor in series arrangement is known as an RC circuit. The capacitor does charge to the potential of the battery however the resistor inflicts a time delay on the charging process. The equation for this is T=RC. t in seconds, r in ohms, and c in farads. The time result however is not the time that it takes for the capacitor to fully charge. This is an important note, the time is the time it takes for the capacitor to charge to 2/3 of its capacitance.For example if the equation gives you 10 seconds, at that interval the capacitor will charge 2/3 of the supplied voltage. Then if left connected for ten more seconds the capacitor charges up to 2/3 of the remaining voltage, and so on and so forth, so in theory the capacitor never fully charges but for practical purposes you can consider your capacitor charged after 3-4 intervals. The function that represents the charging of a capacitor in a RC circuit is an exponential growth function and the fact that it approaches a number very closely but never reaches it, is one of its key properties.
