EBK ENGINEERING FUNDAMENTALS: AN INTROD
EBK ENGINEERING FUNDAMENTALS: AN INTROD
5th Edition
ISBN: 9780100543409
Author: MOAVENI
Publisher: YUZU
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Chapter 12, Problem 23P
To determine

Find the current in each branch in the circuit.

Expert Solution & Answer
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Answer to Problem 23P

The current in the branch R1 is 1.3A.

The current in the branch R2 is 0.73A

The current in the branch R3 is 0.57A.

Explanation of Solution

Given data:

The value of the resistance R1 is 3Ω.

The value of the resistance R2 is 7Ω.

The value of the resistance R3 is 9Ω.

The supply voltage in the circuit is 9V.

Formula used:

Formula to calculate the equivalent resistance in the circuit is,

1Requivalent=1R2+1R3 (1)

Here,

R2 is the resistance value of the resistor 2.

R3 is the resistance value of the resistor 3.

Formula to calculate the total resistance in the circuit is,

Rtotal=R1+Requivalent (2)

Here,

Requivalent is the equivalent resistance.

R1 is the resistance value of the resistor 1.

By using ohm’s law to find the voltage V is,

V=ItotalRtotal

Here,

Itotal is the total current.

Rearrange the equation for the total current as,

Itotal=VRtotal (3)

By using current division rule to find the unknown current I2,

I2=Itotal(oppositeresistanceTotalresistance)=Itotal(R3R2+R3) (4)

By using current division rule to find the unknown current I3,

I3=Itotal×(oppositeresistanceTotalresistance)=Itotal×(R2R2+R3) (5)

Calculation:

Refer to Figure 12.16 in textbook for the example problem 12.6, redraw the circuit by replacing the light bulbs with resistors as shown in Figure 1, the 3Ω resistor is connected in series with a parallel combination of 7Ω and 9Ω resistors.

EBK ENGINEERING FUNDAMENTALS: AN INTROD, Chapter 12, Problem 23P

Substitute 7Ω for R2 and 9Ω for R3 in equation (1) to find Requivalent,

1Requivalent=(17Ω)+(19Ω)=0.2538ΩRequivalent=10.2538Ω=3.9Ω

Substitute 3.9Ω for Requivalent and 3Ω for R1 in equation (2) to find Rtotal,

Rtotal=(3Ω)+(3.9Ω)=6.9Ω

Substitute 9V for V and 6.9Ω for Rtotal in equation (3) to find the current Itotal,

Itotal=9V6.9Ω=1.3A

Therefore, the total current in the circuit is 1.3A.

The current through the resistor R1 is,

Itotal=I1=1.3A.

Substitute 1.3A for Itotal, 7Ω for R2 and 9Ω for R3 in equation (4) to find the unknown current I2,

I2=(1.3A)(9Ω7Ω+9Ω)=(1.3A)(0.5625Ω)I2=0.73A

Substitute 1.3A for Itotal, 7Ω for R2 and 9Ω for R3 in equation (5) to find the unknown current I3,

I3=(1.3A)(7Ω7Ω+9Ω)=(1.3A)(0.4375Ω)I3=0.57A

Conclusion:

Thus,

The current in the branch R1 is 1.3A.

The current in the branch R2 is 0.73A

The current in the branch R3 is 0.57A.

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