RC Circuits Physics Problems, Time Constant Explained, Capacitor Charging and Discharging

in this video we're going to talk about capacitors particularly when they're charging and discharging so let's say if we have an RC circuit that is a circuit containing a capacitor with a resistor and we're going to have an open switch initially let's say that the voltage of the battery is 12 volts this is the resistor R and here we have the capacitor represented by the symbol C now once the switch is closed charge will begin to flow current will flow from the positive terminal of the battery to charge the capacitor the longer side is the positive terminal now keep in mind though electrons they flow in the opposite direction electrons flow from the negative terminal and it enters the positive initially when it switch is open the voltage of the capacitor will be zero as soon as the switch is closed when T is zero the voltage will still be zero but the voltage across the resistor initially will equal the voltage of the value which is 12 now after some significant time has passed the capacitor will be be fully charged let's call it V final it's going to have a final voltage of 12 when the capacitor is fully charged the voltage across the resistance is going to be zero the reason being is once you once the capacitor is fully charged no current will flow in the circuit and if there's no current flowing through the resistor the voltage across that resistor will be zero so initially when a capacitor has a voltage of zero the voltage of the resistor will be 12 because it has to add up to the batter's voltage when the capacitor is the voltage across the resistor will be zero because at that point there's no current flowing through the circuit and keep in mind no current actually passes through the capacitor the current that flows through the circuit is simply used to pump charge from one plate of the capacitor to the other plate the equ equation that describes a capacitor trien is this equation it's equal to the EMF of the battery which in this problem is 12 * 1 minus E E is basically the inverse of the natural log function