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- Two resistors in series have the same current so with Ohm's law,
ΔV

becomes_{eq}= ΔV_{1}+ ΔV_{2}R

Two resistors in parallel have the same voltage drop so with Ohm's law,_{eq}= R_{1}+ R_{2}I

becomes_{eq}= I_{1}+ I_{2}1/ R

_{eq}= 1 / R_{1}+ 1 / R_{2} - Conservation of charge gives
**Kirchhoff's junction rule**: Σ_{junction}I = 0.Conservation of energy gives

**Kirchhoff's loop rule**: Σ_{closed loop}ΔV = 0. - In an
**RC circuit**we have from the loop rule:V - q / C - I R = 0

If q(0) = 0 and V > 0 (charging),(q - C V) = - R C dq / dt

dq / (q - C V) = - dt / (R C)

ln (q - C V) = a - t / (R C)

q(t) = C V + b e

^{ - t / (R C)}q(t) = C V (1 - e

If q(0) = Q and V = 0 (discharging),^{ - t / (R C)})q(t) = Q e

The^{ - t / (R C)}**time constant**is τ ≡ R * C.This plot shows the current (dq/dt) charging the capacitor in blue and the current through the resistor in red:

Note that as the capacitor charges, the current shifts from it to the resistor. When the capacitor is fully charged, it is effectively open and all of the current flows through the resistor.

- This applet will allow you to practice analysis of some simple RC networks.

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©2012, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

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