25.6
Energy Stored in a Capacitor: Problem Solving
In 1749, Benjamin Franklin coined the word battery for a series of capacitors connected to store energy. Capacitors store electric potential energy th…
Capacitors act as temporary batteries storing electric potential energy that could be released over a short time.
In small engines, a capacitor-discharge ignition system is used that consists of a charging unit to charge a capacitor completely. Upon receiving a trigger, the capacitor rapidly discharges the stored energy to an ignition coil that, in turn, fires the spark plug to start the engine.
The amount of energy stored by a capacitor-discharge ignition system depends on the value of the applied voltage and the capacitance of the capacitor.
Consider a fully charged capacitor with a charge of 375 micro coulomb and capacitance of 1.5 micro farad. Here the charge and capacitance are known quantities, and the voltage and energy are unknown quantities.
Using the known quantities, the voltage supplied to the system could be calculated to be 250 volt.
Upon substitution, the voltage and capacitance values give the value of the electric potential energy saved in the capacitor to be 0.047 joules.
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Q1: How does a capacitor-discharge ignition system work in small engines?
A capacitor-discharge ignition system charges a capacitor completely using a charging unit. Upon receiving a trigger, the capacitor rapidly discharges its stored energy to an ignition coil, which then fires the spark plug to start the engine. This system efficiently converts stored electric potential energy into the spark needed for combustion.
Q2: What parameters determine the energy stored in a capacitor?
The energy stored in a capacitor depends on the applied voltage and the capacitance value. If you know any two of the three related parameters—voltage, charge, or capacitance—you can calculate the unknown parameter and determine the total electric potential energy stored in the system.
Q3: How do you calculate voltage from charge and capacitance values?
Voltage is calculated by dividing the charge by the capacitance using the relationship between these three parameters. For example, a capacitor with 375 microcoulombs of charge and 1.5 microfarad capacitance yields a voltage of 250 volts. This relationship allows you to find any unknown parameter when two are known.
Q4: What is the formula for calculating electric potential energy in a capacitor?
Electric potential energy stored in a capacitor can be calculated using the values of capacitance, voltage, and charge. In a typical problem, a fully charged capacitor with 1.5 microfarad capacitance and 250 volts stores 0.047 joules of energy. This energy can be released rapidly when the capacitor discharges.
Q5: Why are capacitors useful for temporary energy storage applications?
Capacitors store electric potential energy that can be released over a short time, making them ideal for applications requiring rapid energy discharge. This property enables their use in capacitor-discharge ignition systems and other applications where quick bursts of electrical energy are needed to trigger or power devices.
Q6: What historical significance do capacitors have in electrical engineering?
In 1749, Benjamin Franklin coined the word battery to describe a series of capacitors connected to store energy. This terminology reflects the early recognition of capacitors' ability to accumulate and hold electrical charge, establishing the foundation for modern energy storage technology and electrical circuit design.
Q7: How do you solve for unknown capacitor parameters in problem-solving scenarios?
To solve for unknown parameters, identify which two of the three related values—voltage, charge, or capacitance—are known. Use the mathematical relationships between these parameters to calculate the unknown value, then apply the energy formula. This systematic approach works for any capacitor system, including capacitor-discharge ignition applications.