CourseNotes.30 - Figure 23 Three Resistors in Series with...

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Figure 23: Three Resistors in Series with Their Simplified Equivalent Resistor Figure 24: Three Resistors in Parallel with Their Simplified Equivalent Resistor Next, we pass through the three resistors at each of which we lose iR i in potential. After that, we find ourselves back at point b and therefore V - iR 1 - iR 2 - iR 3 = 0 V = iR 1 + iR 2 + iR 3 V = i ( R 1 + R 2 + R 3 ) By comparing the last form of the expression with Ohm’s law, we can see what the resistance of our simplified resistor is. For n resistors in series, the equivalent simplified resistor is R eq = n X j =1 R j (26) We now want to do the same thing, except for multiple resistors in parallel (see figure 24). In this case, we will use the fact that since opposite sides of each resistor are wired to opposite sides of the battery, the potential difference across each resistor must be the same. We will also use the fact noticed above that the sum of the currents through each resistor must be equal to the current flowing through the rest of the circuit (the battery in this case).
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