   Chapter 18, Problem 9P

Chapter
Section
Textbook Problem

Two resistors connected in series have an equivalent resistance of 690 Ω. When they are connected in parallel, their equivalent resistance is 150 Ω. Find the resistance of each resistor.

To determine
The resistance of the individual resistor.

Explanation

Given Info: The equivalent resistance of the two resistors connected in series and parallel is RS=690Ω and RP=150Ω .

Explanation:

If the two resistors are connected in series, then the equivalent resistance is,

RS=R1+R2

• RS is the equivalent resistance of the series combination of resistors,
• R1 and R2 is the resistors connected in series,

Substitute 690Ω for RS .

R1+R2=690Ω (1)

Rewrite the equation (1) in terms of R2 .

R2=690ΩR1 (2)

If the two resistors are connected in parallel, then the equivalent resistance is,

1RP=1R1+1R2

• RP is the equivalent resistance of the parallel combination of resistors,
• R1 and R2 is the resistors connected in parallel,

Rearrange the above relation of equivalent resistance as,

RP=R1R2R1+R2

Substitute 150Ω for RP

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