RC Circuits and Household Wiring

This lecture is based on Serway, Sections 28.4 and 28.6.

When a capacitor in series with a resistor discharges, the charge on its plates decreases exponentially
```
         q(t) = q0 * exp(-t/RC)
```
The current created by the capacitor also decreases exponentially from its initial value
```
         I(t) = I0 * exp(-t/RC)
```
The product of resistance and capacitance, RC, is called the time constant of the circuit. The current and charge change by a factor of e (= 2.718) for every time constant which passes
Charging a capacitor goes quickly at first, then slows down and approaches a limiting value
```
         q(t) = q0 * [ 1 - exp(-t/RC) ]
             
              = CV * [ 1 - exp(-t/RC) ]
```
where V is the voltage of the battery charging the capacitor
The current flowing as a capacitor charges is large at first, but decreases with time
```
         I(t) = I0    * exp(-t/RC) 

              = (V/R) * exp(-t/RC)
```
Typical houses contain several circuits, all connected in parallel to the external power supply. Each circuit is rated to carry at most a certain current (typically 10 to 30 amps)
Each circuit contains a circuit breaker, or a fuse, to prevent larger currents from flowing