DC Circuits 2 Overview

We are going to look in detail at what happens in circuits with capacitors and resistors together. We will need to use the Kirchoff Rules to investigate these circuits. In any circuit, the principles of conservation of charge and conservation of energy play a key role and form the basis of our analysis. We will see how these principles lead to Kirchoff's rules.

Conservation of Charge

The idea of conservation of charge is pretty simple. All branches of a circuit connect at junctions. Conserving charge means that the sum of the current flowing into the junction must balance the sum of the currents flowing out of the junction. Watch the charges in the animation below:

Particles coming from one branch flow into the other two branches, so that

I(in) = I(out 1) + I(out 2)

Conservation of Energy

If the electric field is conservative, then the sum of the potential drops around a closed loop must be zero.

These two principles form Kirchoff's rules.

Application of Kirchoff's rules

• Choose a current and direction for each branch of the circuit. It doesn't matter if you choose the direction of the physical current. If you do not your answer will be negative. You can use your finger to trace through a circuit. Everytime your finger hits a junction you will need new currents unless it connects back to a branch you have already covered.
• Mark the polarities in the circuit. The largest plate on the battery symbol is the positive plate. The direction you chose for the current determines the polarity of the resistor. Current always flows downhill through a resistor.
• Choose the closed loops. Each loop must contain a circuit element not contained by any other loop.
• Sum the potential rises and drops around each closed loop.
• Apply charge conservation to each junction being careful to keep the equations independent.

Keep these in mind as we do the exercises today.

Go to Exercise 1.

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