W9_parallel_resonance.eps

Week 5: Resistance 181

junction itself cannot act as a reservoir for charge – it has negligiblecapacitance because it is part
of a continuous volume of (presumed perfect) conductor that can conduct any charge surplus of the
(incompressible) charge away as rapidly as it develops.

This means that all the charge goingintothe junction has to gooutof the junction along the
various wires that join together at the junction. This rule can be written, and thought of, in two
different ways:

I 1 ,in−I 2 ,out−I 3 ,out−I 4 ,out= 0 (344)

with theconventionthat current goingintothe junction is positive and current comingoutof the
junction is negative. Alternatively, you can sort out the currentscoming in and the currents going
out and equate them:

I 1 ,in=I 2 ,out+I 3 ,out+I 4 ,out (345)

Note that these two equations are the same.

Let us generalize the first form to:

junction∑

i

Ii= 0 (346)

and call itKirchhoff’s Junction Rule(using the±convention). Remember, the junction rule is just
the symbolic expression of charge conservation, just as the loop rule is the symbolic expression of
energy conservation.

Just for grins, let’s put both rules down side by side, the way you should probably remember
them:

loop∑

i

Vi = 0 Loop Rule (347)

junction∑

i

Ii = 0 Junction Rule (348)

Example 5.4.1: The Internal Resistance of a Battery

V

R

0

Battery

Load

+

−

V

terminals

terminal

r

Figure 58: A non-ideal battery in a circuit with a resistive load.

Previously, we indicated that any real battery (or electrical power supply, not necessarily a
battery) is incapable of doing aninfiniteamount of work or deliving aninfiniteamount of power.
If you put a load of any sort on a real battery, you can increase the load (the power draw) up to
a point, but if you try to drawmore power than the battery can deliver, the net power delivered to
the load will actuallydecrease.

This is actually a key principle of electrical design, where one often wishes to deliver themaximum
power to some load – a speaker, a radio antenna, even a light bulb – that the power supply will
support.