Capacitors in Circuits

Some applications Storing large amounts of charge for later release e.g., camera flash, defibrillator Computer interface components e.g., touch screen, keyboards Protecting components from surges in direct current e.g., adapters, surge protectors Uninterrupted power supply e.g., power for computers and other electronic devices with changing load requirements In conjunction with resistors, timing circuits e.g., pacemakers or intermittent windshield wipers Etc. Virtually every piece of modern electronics contains capacitors. Read more here:

Connecting capacitors

V battery = V resistor + V capacitor where V resistor = IR V capacitor = Q/C V b = IR + Q/C Voltage of a charging capacitor

t = 0 s V b = IR + Q/C When you first close the switch, the capacitor has no charge. You can evaluate the circuit as if the capacitor were a wire. In this case, the resistor must dissipate all of the battery’s voltage.

t = long time V b = IR + Q/C Long after you close the switch, there is the capacitor is fully charged and has the ~ same voltage as the battery. Therefore, there is ~no current through the resistor.

0 s < t < long time  time, capacitor charges  potential difference between battery and capacitor  current through resistor

Mathematical model The product of resistance and capacitance (RC) is sometimes called the “time constant” of the circuit and is abbreviated with the Greek letter tau, 

Current through a resistor in a charging RC circuit Initial current: 100 A Current decreases exponentially as potential difference between battery and capacitor gets smaller 37% max after 1 time constant

Example 1

Example 2

0 s < t < long time  time, capacitor charges  potential difference between battery and capacitor  rate at which charge accumulates at capacitor

Mathematical model Recall that capacitance is a ratio of charge per volt, C = Q / V

Charge on a capacitor in a charging RC circuit Initial charge: 0 C Slope of line (charge / second = current) approaches zero as capacitor gets charged 63% max after 1 time constant

Example 1

Example 2

Summary for a charging RC circuit

@ t = 0, switch is closed. Energy stored in capacitor pushes charge through resistor, doing work. Over time, potential difference drops, pushing less current through resistor. Voltage of a discharging capacitor

Mathematical model of discharging RC circuit

Applications Use an RC circuit to regularly charge and discharge to produce voltage pulses at a regular frequency.

Example