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3.2 Effective Resistance of Network
You can use this interactive lab to practice calculating the equivalent resistance of the network of
resistors connected in different ways, in series or parallel.
Whenever you see a complicated network such as the one in this demonstration, try to analyze
how the individual resistors or the groups of resistors are connected to each other. Start with the
network as a whole, and break it up into smaller pieces.
Step 1: How is the fifth resistor, R5, connected to the network of the resistors one through
four? Write the equivalent resistance in terms of R1234 and R5. (Compare your work with the
solution at the end of the worksheet.)
Step 2: Within the network of the resistors one through four, how is the resistor four, R4,
connected to the group of resistors one, two, and three? Write R1234 in terms of R4 and R123.
Step 3: Repeat the process and write the equivalent resistance of the group of resistors one,
two, and three, R123, in terms of R1 and R23.
Step 4: Finally, express R23 in terms of R2 and R3. Now you can work backwards and
calculate the equivalent resistance R12345 when given R1, R2, R3, R4, and R5.
Pick various values for the resistances of each resistor, and calculate the effective resistance of
the network using the formula you derive. Record your work in the table below, and check if
your results are always the same as in the demonstration.
R1 R2 R3 R4 R5 R12345
R12345
(calculated) (shown in demo)
1)
2)
3)
Solution:
Step 1: Series: 𝑅12345 = 𝑅1234 + 𝑅5
Step 2: Parallel: 𝑅1234 =
1
1
𝑅123
𝑅 𝑅123
+𝑅 =𝑅4
123 +𝑅4
4
Step 3: Series: 𝑅123 = 𝑅1 + 𝑅23
Step 4: Parallel: 𝑅23 =
1
𝑅3
1
𝑅 𝑅
+ 𝑅 = 𝑅 2+𝑅3
2
2
3