   Chapter 18, Problem 20P

Chapter
Section
Textbook Problem

For the circuit shown in Figure P18.20, calculate (a) the current in the 2.00-Ω resistor and (b) the potential difference between points a and b, ΔV= Vb− Va. Figure P18.20

(a)

To determine
The current in 2.00Ω resistor.

Explanation

Given Info:

Resistance R1 is 4.00Ω , Resistance R2 is 2.00Ω , Resistance R3 is 6.00Ω , Voltage ε1 is 12.0V , and Voltage ε2 is 8.00V .

Explanation:

Below Figure shows the direction of current in the circuit

• ε1,ε2 is voltage in the circuits
• R1,R2,R3 is corresponding resistance in the circuits
• I1,I2,I3 is corresponding current in the circuits

Apply Kirchhoff’s voltage law to the left and right loop.

From the upper loop

ε1R1I1R2I2=0

Substitute, 4.00Ω for R1 , 2.00Ω for R2 , and 12.0V for ε1 in the above equation to find expression for I1

12.0V4.00ΩI12.00ΩI2=012.0V(2.00Ω)I2=4.00ΩI13.00V(0.500Ω)I2=I1

From the lower loop

ε2+R2I2R3I3=0

Substitute, 2.00Ω for R2 , 6

(b)

To determine
The potential difference between point a and b.

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