10-15-14 DC circuit analysis

This is Carl Friedrich Gauss. Badass.

This is the application of gauss's law and other formula's. It was left on the board after someone else's class. Gotcha.

This the equations for circuits. resistance vs capacitance. series vs parallel.

• Determine which branches of the circuit have a different current flowing through them and attach labels to the currents flowing in each branch. Components in series will have the same current so there is no need to use more than one label in a series branch.
• Assume a direction for the current flow in each branch of a circuit. You do not have to know which way the current is actually flowing for your solution to be correct. If you choose the wrong direction and do the problem correctly, you will get a negative answer of the current. Meaning that the current is flowing opposite to your initial assumption.
• Apply Kirchhoff' s Current Rule to the circuit junctions. This means write down the equation(s) that relate the currents flowing into that junction with the currents out of that junction.
• Choose a closed loop in the circuit and pick a direction around the loop. Your choice is arbitrary in that you should get a correct solution no matter which direction you pick for the loop - either clockwise or counterclockwise. It will make the solution less confusing if you can chose the loop in the same direction as the current is flowing. However, it is often not possible to do this for every section of the loop
• Apply Kirchhoff's Voltage Rule to the loop. This means pick a starting point in a loop and go around it and write down the voltage gains and drops until you return to your starting point. It some instances a battery can be a voltage drop rather than a gain if its polarity is opposite loop direction you have chosen.
• If you have several variables to determine, you may need to choose additional loops and repeat the above. In the end you need to generate a set simultaneous linear equations to solve, one for each unknown variable that you will have to solve.

Remembering the Code:  There are a number of ditties that have been devised to help people remember the resistor code.  Some of them are too “colorful” for official publication and others are too boring.  A good compromise is found in the ditty “Bad Booze Rots Our Young Guts But Vodka Goes Well” in which the BBROYGBVGW sequence of first letters matches that for Black, Brown, Red, etc.

Kirchhoff’s Laws 1.   Junction (or node) Rule (based on charge conservation):  The sum of all the currents entering any node or branch point of a circuit (that is, where two or more wires merge)must equal the sum of all currents leaving the node. 2.   Loop Rule (based on energy conservation):  Around any closed loop in a circuit, the sum of all emfs, voltage gains provided by batteries or other power sources, (e = emf) and all the potential drops across resistors and other circuit elements must equal zero.

Kirchhoff’s Laws

1.   Junction (or node) Rule (based on charge conservation):  The sum of all the currents entering any node or branch point of a circuit (that is, where two or more wires merge)must equal the sum of all currents leaving the node.

2.   Loop Rule (based on energy conservation):  Around any closed loop in a circuit, the sum of all emfs, voltage gains provided by batteries or other power sources, (e = emf) and all the potential drops across resistors and other circuit elements must equal zero.

The center bulb will remain OFF. Because the two sides of the circuit connected by the middle wire are at the same potential, no current can flow in that wire, and the bulb will not be lit.

The fundamental feature for this circuit is that the potentials at the points on opposite sides of the switch are the same before the switch is closed. This can be seen by noting that the two batteries are identical and the two light bulbs are identical. Therefore, closing the switch does not do anything to the circuit.

Two important points are relevant to the explanation of this result. First, note that the potential at the point where the third battery joins the circuit of the other two remains the same when the switch is closed. This is so because all of the batteries are the identical, and the potential along the light bulb wire is divided equally between the bulbs because they are identical. Therefore, closing the switch does not do anything to the circuit.