This Set o’ Slides - Day 17, Friday, Feb 12
• Kirchhoff’s Rules
• Analyzing Circuits Examples
• Internal Resistance

Solving Circuits with Kirchhoff’s Rules
• Draw out the circuit.
• Draw the current in each branch of the circuit. Generally, in the direction you believe the current goes, but , the direction is arbitrary. If you choose incorrectly, your calculations will result in a negative value, meaning the correct direction is opposite your chosen direction.
• Mark each resistor end with a plus and minus sign, based on your chosen current direction. Outside of a battery, current always flows from higher (+) potential to lower (-) potential
• Apply the junction rule at all junctions.

Solving Circuits with Kirchhoff’s Rules
(continued)
• Assign loop directions for each loop. Direction is arbitrary; you’ll get the same (correct) answer either way. Generally, loop from – to + through batteries when possible. This is for intuition’s sake and isn’t necessary.
• Apply the loop rule going in the direction chosen.
Σ V drops
=
Σ
V rises
Potential difference in resistors is given by Ohm’s Law:
V=IR.
Potential difference in batteries is given by size of battery.

Solving Circuits with Kirchhoff’s Rules
(continued)
• Looping rule continued:
Looping through any device from + to – is a V drop
.
Looping through any device from – to + is a V rise
.
A loop that goes against the current in a resistor signifies a potential rise, V rise
.
• Obtain as many equations as unknowns.
• Solve equations simultaneously.
• Check.
Double-check potential sum in loop.
Check if/that P input
= P output
.

Internal Resistance and Terminal Voltage
• Devices that provide emf, batteries and generators for example, also have their own internal resistance .
• This resistance can be thought of as a separate resistor in series with the device and the circuit.
• This lowers the output voltage from its nominal value .
• The output voltage is called the terminal voltage (since it’s measured at the terminals.) It’s dependent on the total current being drawn from the source (battery).
V terminal
= E – I R internal
• A voltmeter might register adequate voltage (emf), but, a voltmeter draws little/no current. The battery looks good, but, when current is drawn from battery, the terminal voltage drops to low levels.
• This is why the best battery test is a load test.