A simple case of a charging circuit is a resistance-capacitor circuit. For example, consider a circuit that is made up of a battery, resistor and an uncharged capacitor in series with a switch that breaks the conducting path of the closed circuit if it is open. If the switch is closed then current can flow around the circuit. Initially, the current I is at its maximum and is given by the voltage of the battery V divided by the resistance of the Resistor R. Then, as time passes, the charge q on the capacitor grows. As the capacitor charges, the current through the circuit decreases and when the capacitor is fully charged the current decreases in value to zero. Amperage is a measurement of current.

 

 

1. Calculate the time constant, otherwise known as the relaxation time. The time constant T is given by the product of the resistance R and the capacitance C as follows: T= R*C seconds. For example, if C =1e-6 Farads (with e a notation to indicate an exponent), R=10e6 Ohms then the time constant is T = 1e-6*10e6 = 10 seconds. This value is an indication of how quickly the capacitor charges.

 

2. Calculate the maximum value of the current. The maximum value of the current I can be found when the switch is initially closed, and is given by the value I = V/R Amperes, where, again, R is the resistance and V is the voltage across the battery charger. For the current example, where V = 12 V and R = 10e6 Ohms, the current I is 12/10e6 = 1.2e-6 Amperes.

 

3. Calculate the instantaneous current at a given time after the switch has been closed. Call the instantaneous current i. This is related to the maximum value of the current I through the formula i = I*exp(-t/T) A, where T is the time constant, t is the elapsed time beyond when the switch was closed and exp() is the exponential function. For the current example, where C = 1e-6 Farads, R = 10e6 Ohms and the voltage across the battery is 12 V, the initial value of the current after the switch has been closed was determined from step two to be 1.2e-6 A, the time constant from step one is 10 seconds and the instantaneous current at time t is i = 1.2e-6exp(-t/10) Amps. If 5 seconds have passed since the switch was closed then the instantaneous current is i=1.2e-6exp(-5/10) Amps. The exp function is found on most calculators and you should get exp(-5/10)=0.606, which makes the instantaneous current i = 1.2e-6*0.606 = 0.727e-6 Amps.