   Chapter 18, Problem 27P

Chapter
Section
Textbook Problem

(a) Can the circuit shown in Figure P18.27 be reduced to a single resistor connected to the batteries? Explain. (b) Calculate each of the unknown currents I1, I2, and I3 for the circuit. Figure P18.27

(a)

To determine
To reduce the circuits to a single resistor connected to the batteries.

Explanation

Given Info: Resistance R1 is 2.0Ω , Resistance R2 is 4.0Ω , Resistance R3 is 3.0Ω Resistance R4 is 1.0Ω , Resistance R5 is 5.0Ω .

Explanation:

Some simplification can be made to reduce the circuit.

Formula to calculate to reduce to a single resistor is by equivalent resistance REq upper in series

From the Upper loop:

Two resistances are connected in series R1 and R2

REq upper=R1+R2 (I)

Formula to calculate to reduce to a single resistor is by equivalent resistance REq lower in series

From the lower loop:

Two resistances are connected in series R4 and R5

REq lower=R4+R5 (II)

• REq upper is Equivalent resistance in the upper loop
• REq lower is Equivalent resistance in the lower loop
• R1,R2,R3,R4,R5 is corresponding resistance in the circuits
• I1,I2,I3 is corresponding current in the circuits

Substitute 2

(b)

To determine
The current from the circuits I1,I2,I3 .

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