Thursday, April 16, 2015

Everything is Relative

Relativity.  It’s not just for solving astronomical phenomena, but can also be applied to solving circuits.  The observer in this case is you! – The circuit solver. 

Sometimes as an observer you have to guess the direction of current in a network – just like the network seen in Figure 1.

Figure 1. Guessing current direction in resistor network

  The great thing about relativity is that as long as you follow the rules below you’ll be able to obtain a correct expression of the circuit.  Just remember what you learned in the KCL section and you’ll be all set – current flowing in equals current flowing out.  Another important rule to follow is that current can only flow in one direction while traveling through a wire.

The first step is to pick the polarity of the current.  Is the current flowing into a node mathematically shown as positive or negative?  In most texts, the current flowing into a node is assigned to be a negative quantity, while the current flowing out of a node is chosen to be a positive value.  Again, the choice is yours, just make sure to follow it otherwise it can confuse you in the long run.  For our future circuits, we will respectively choose current flowing in to and out of a node as a negative and positive value.  

In any circuit, the true direction of the current will reveal itself once you plug in numerical values.  Using the example circuit from Figure 1, let’s plug in 5V for V1, and 2V for V2, the updated circuit is shown in Figure 2.

Figure 2. Current calculation in the above networks

Notice that the calculations verify if our guess was correct or not, if the current value turns out to be a positive value the direction we guessed was correct.  If the current is a negative value, we now know that current is flowing in the opposite direction.

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