RC Circuit Formula Derivation: Solving the Differential Equation Using an Integrating Factor

Analysis of one of the basic building blocks of electronic circuitry

© Eugene Brennan

What are Capacitors Used For?

Capacitors are used in electrical and electronic circuitry for a variety of reasons. Typically these are:

• Smoothing of rectified AC, pre-regulation in DC power supplies
• Setting the frequency of oscillators
• Bandwidth setting in low pass, high pass, band pass and band reject filters
• AC coupling in multistage amplifiers
• Bypassing transient currents on power supply lines to ICs (decoupling capacitors)
• Starting of induction motors
• EMI (Electromagnetic Interference) suppressors in electronic devices and electrical appliances

Time Delays in Electronic Circuits

Whenever capacitance and resistance occurs in an electronic or electrical circuit, the combination of these two quantities results in time delays in transmission of signals. Sometimes this is the desired effect, other times it may be an unwanted side effect. Capacitance may be due to an electronic…