INTRO TO PHYSICAL SCIENCE W/MINDTAP
INTRO TO PHYSICAL SCIENCE W/MINDTAP
14th Edition
ISBN: 9781337077026
Author: Shipman
Publisher: CENGAGE L
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Chapter 8, Problem 1VC
To determine

The current passing through each resistor and a parallel circuit combination.

Expert Solution & Answer
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Answer to Problem 1VC

The current passing through each resistors are 1 A for Ia , 2 A for Ib and 2 A for Ic and the total current passing through a parallel circuit is 5 A for Id .

Explanation of Solution

Given info: First resistor having resistance 12 Ω , second resistor having resistance Ω , third resistor having resistance Ω and dc voltage source is 12 V .

Explanation:

The figure represents a parallel circuit arrangement. In a parallel circuit three resistors are arranged with their heads connected to head and tails are connected tails across the dc voltage source as shown in below figure.

INTRO TO PHYSICAL SCIENCE W/MINDTAP, Chapter 8, Problem 1VC

Formula to calculate the equivalent resistance in a parallel circuit is,

1RP=1R1+1R2+1R3RP=(R1)(R2)(R3)R2R3+R1R3+R1R2

Here,

R1,R2,R3 are the resistances for individual resistors

Substitute 12 Ω for R1 and Ω for R2 and Ω for R3 .

RP=(12 Ω)(Ω)(Ω)(Ω)(Ω)+(12 Ω)(Ω)+(Ω)(12 Ω)=432 Ω36 Ω+72 Ω+72 Ω=432 Ω180 Ω=2.4 Ω

The current passing through a parallel circuit is divided among each resistor.

The expression for the total current passing through each resistor is,

Id=Ia+Ib+Ic (1)

Here,

Ia,Ib,Ic are the current passings through each resistor

Id is the total current flowing through a parallel circuit

Write the expression for current in terms of voltage and resistance in a resistor having resistance R1 .

Ia=VR1

Here,

V is the dc voltage source across the parallel circuit

Substitute 12 V for V and 12 Ω for R1 to get Ia .

Ia=12 V12 Ω=1 A

Write the expression for current in terms of voltage and resistance in a resistor having resistance R2 .

Ib=VR2

Substitute 12 V for V and 6 Ω for R2 to get Ib .

Ib=12 V6 Ω=2 A

Write the expression for current in terms of voltage and resistance in a resistor having resistance R3 .

Ic=VR3

Substitute 12 V for V and 6 Ω for R3 to get Ic .

Ic=12 V6 Ω=2 A

The expression for the total current passing through each resistor is,

Id=Ia+Ib+Ic (2)

Substitute VR1 for Ia , VR2 for Ib and VR3 for Ic in equation (2).

Id=VR1+VR2+VR3

Substitute 12 V for V , 12 Ω for R1 , 6 Ω for R2 and Ω for R3 to get Id .

Id=12 V12 Ω+12 VΩ+12 VΩ=(12 V)(112 Ω+16 Ω+16 Ω)=(12 V)((Ω)(Ω)+(12 Ω)(Ω)+(12 Ω)(Ω)(12 Ω)(Ω)(Ω))

Further solve the equation.

Id=(12 V)(180 Ω432 Ω)=2160 V432 Ω=5 A

Conclusion:

Therefore, the current passing through each resistor is 1 A for Ia , 2 A for Ib and 2 A for Ic and the total current passing through a parallel circuit is 5 A for Id .

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Chapter 8 Solutions

INTRO TO PHYSICAL SCIENCE W/MINDTAP

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