I've updated our "learning equations" discussion over on the Tips page, so I wanted to share it here. Generally I avoid mnemonics when it comes to equations, but I've added an example of how I'd memorize 4/3 pi r^3 with memory techniques at the bottom.
As usual, these tips represent our personal experience and should be taken with a grain of salt. Having your own learning goals, you may find it necessary to memorize full equations, and if you decide to go that route, more power to you. I just haven't found it necessary to memorize full equations for the specific courses I've taken. As an illustration, here's how I'd memorize a full equation:
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Locus #1: A large sphere to encode the equation's purpose. Simple as that. Maybe it's banging into things or simply spinning in place. [I sometimes skip this step, as I've found that after a few reviews I automatically associate the loci with the relevant topic anyway.]
As discussed in Lesson 1, the electrochemical cell of a circuit supplies energy to the charge to move it through the cell and to establish an electric potential difference across the two ends of the external circuit. A 1.5-volt cell will establish an electric potential difference across the external circuit of 1.5 volts. This is to say that the electric potential at the positive terminal is 1.5 volts greater than at the negative terminal. As charge moves through the external circuit, it encounters a loss of 1.5 volts of electric potential. This loss in electric potential is referred to as a voltage drop. It occurs as the electrical energy of the charge is transformed to other forms of energy (thermal, light, mechanical, etc.) within the resistors or loads. If an electric circuit powered by a 1.5-volt cell is equipped with more than one resistor, then the cumulative loss of electric potential is 1.5 volts. There is a voltage drop for each resistor, but the sum of these voltage drops is 1.5 volts - the same as the voltage rating of the power supply. This concept can be expressed mathematically by the following equation:
The mathematical analysis of this series circuit involved a blend of concepts and equations. As is often the case in physics, the divorcing of concepts from equations when embarking on the solution to a physics problem is a dangerous act. Here, one must consider the concepts that the current is everywhere the same and that the battery voltage is equivalent to the sum of the voltage drops across each resistor in order to complete the mathematical analysis. In the next part of Lesson 4, parallel circuits will be analyzed using Ohm's law and parallel circuit concepts. We will see that the approach of blending the concepts with the equations will be equally important to that analysis. be457b7860
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