Consider computing the discharge of a capacitor to determine its voltage, current and stored energy as time goes by. Capacitors store electrical energy in circuits for later use. This energy may be dissipated as heat through a resistor that blocks the flow of electrical current. In basic form, a capacitor consists of a pair of parallel metal plates encased in plastic. The amount on energy stored on the capacitor depends on its capacitance in farads and its voltage. When a capacitor discharges, it does so at an exponential rate.

- Skill level:
- Moderate

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## Instructions

- 1
Multiply the resistance, in ohms, by the capacitance of the circuit, in farads, to obtain the time constant in seconds for the circuit. The time constant represents the time for the charge on the capacitor to drop to 36.79 per cent of its original value. Assume a resistance of 200 ohm and a capacitance of 100 microfarad. A microfarad, a common capacitance unit, equals one millionth of a farad. Performing this step leads to a time constant of 200 times 100 times 10^-6, or 0.02 seconds. The symbol "^" denotes an exponent and is read as "to the power."

- 2
Divide the time, in seconds, that passed during discharge by the time constant. Then multiply by minus one. Call this result "X." Assuming a time of 0.01 seconds leads to 0.01 seconds divided by 0.02 seconds, or 0.5. Multiplying by minus one yields -0.5 for "X."

- 3
Take the exponential of "X." Call this result "Y." The exponential function is labelled by either "exp" or "e^x" on calculators. Continuing the exercise leads to the exponential of -0.5, or 0.61 for "Y."

- 4
Multiply the initial voltage on the capacitor by "Y" to obtain its voltage after the partial discharge. Assuming an initial voltage of 5 volts, you have 5 volts times 0.61, or 3.1 volts.

- 5
Divide the new voltage of the capacitor by the resistance to obtain the current in the capacitor in amps after partial discharge. Now you have 3.1 volts divided by 200 ohms, or a current of 0.02 amps.

- 6
Multiply 0.5 by the capacitance by the voltage after partial discharge squared to get the energy stored in the capacitor in joules. Performing this calculation you have 0.5 times 100 times 10^-6 times 3.1 volts times 3.1 volts, or an energy of 0.00048 joules. This is equivalent to 0.48 millijoules, since a millijoule equals 1,000 joules.