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Lesson 4: Reducing Simple Parallel-Series Combination Circuits

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A simple parallel-series circuit

Resistors R2 and R3 are connected in series and make up one branch of a parallel circuit. Resistor R1 is the second branch. The total resistance of this circuit is given by:

RT = R1 || (R2 + R3)

This circuit is reduced to equivalent values by first summing R2 and R3 to get the value of equivalent resistor R2, 3, and then combining R1 with R2, 3 to get the total equivalent resistance, R1,2, 3.

 

Example

Systematically reduce this circuit  to its equivalent resistance.

fig05112101.gif (1874 bytes)

Step 1: Combine resistors R2 and R 3 to form the equivalent resistance, R2, 3.

This is a series combination, so you should sum the resistance values:

R2, 3 = R2 + R3
R2, 3 = 220 W + 180 W = 400 W

fig05112102.gif (1770 bytes)
Step 2: Combine R1 with equivalent resistance R2, 3 to complete the reduction procedure.

This is a parallel combination, so:

R1, 2, 3 = R1 || R2, 3
R1, 2, 3 = 330 W || 400 W = 181 W

 

fig05112103.gif (1488 bytes)


Author and content provider: David L.Heiserman
Publisher: SweetHaven Publishing Services

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