Jul 2, 2011

Series-Parallel Quiz Solution

I only got one answer submission to my quiz from the last blog entry but that was all it took. The equivalent resistance of the circuit I showed in that entry (shown below) is 5 ohms. Let's quickly look at how to break it down.
Step 1: Start at the terminals farthest away from your perspective (in this case we are looking into the circuit from the left). The 1 ohm and 2 ohm resistors are in series with each other so we can combine them into one 3 ohm equivalent resistance. The circuit now looks like Figure 1. 

 Figure 1. Circuit after combining 1 ohm and 2 ohm resistors

Step 2: Keep the same approach (start from the furthest component). Now, the 6 ohm and 3 ohm resistors are in parallel so they can be combined into one resistor using the formula for parallel resistance: 
So far, we have managed to condense the circuit down to Figure 2. 

 Figure 2. Circuit after combining 6 ohm and 3 ohm resistors

Step 3: Does this look familiar by now? The two 2 ohm resistances are in series so we can combine them into one 4 ohm resistor, getting an equivalent circuit like Figure 3 .

 Figure 3. Circuit after combining both 2 ohm resistors

Step 4: We now have the same scenario as in step 2 so we apply the same methodology. *Hint - any time you have two resistances of the same value in parallel, their equivalent resistance will be half the value of the two resistors. In this case, two 4 ohm resistances in parallel results in an equivalent resistance of 2 ohms. Now the circuit has been condensed all the way down to Figure 4.

 Figure 4. Circuit after combining both 4 ohm resistors

Step 5: We're in the home stretch at this point. Add the two resistances in series to get the equivalent resistance looking into the circuit according to the original schematic. Hopefully by now you can see why the equivalent resistance is equal to 5 ohms, but, just to drive the point home, see Figure 5 for the final answer.
 Figure 5. Equivalent circuit after reducing all resistances


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