SOLUTION(a) Find the equivalent resistance of the circuit.R = R, + R, = 8.0 2 + 4.0 2 = 12.0 0eqThe 8.0-2 and 4.0-2 resistors are inseries, so use the sum rule to find theequivalent resistance between a and b.The 6.0-2 and 3.0-0 resistors are in11%3DReq6.0 22.0 QR,Regparallel, so use the reciprocal-sum ruleR,3.0 0to find the equivalent resistance= 2.0 2between b and c (don't forget toinvert!).In the new diagram, figure b, there areR-R, + R, -12.0 Ω+ 2.0 Ω-14.0 Ωeqnow two resistors in series. Combinethem with the sum rule to find theequivalent resistance of the circuit.(b) Find the current in each resistor if a 42-V battery is connected between points a and c.ΔνI =Find the current in the equivalent42 V= 3.0 Aac =Reqresistor in figure c, which is the total14 2current. Resistors in series all carry thesame current, so the value is thecurrent in the 12-2 resistor in figure band also in the 8.0-N and 4.0-2resistors in figure a.Calculate the voltage drop AVparaΔνpara= IR = (3.0 A)(2.0 2) = 6.0 Vacross the parallel circuit, which has anequivalent resistance of 2.0 Q.Apply Ohm's law again to find theΔνpara6.0 V= 1.0 Acurrents in each resistor of the parallel6.0 2R6,0 0circuit.Δνpara6.0 VI2= 2.0 A3.0 2R3,0 0LEARN MOREREMARKS As a final check, note that AV = (6.0 2)I, = (3.0 N)I, = 6.0 V andbcAVh = (12 N)I, = 36 V; therefore, AV= AV + AV = 42 V, as expected.bcасabQUESTION Which of the original resistors dissipates energy at the greatest rate?O the 8.0 2 resistorO the 4.0 2 resistorO the 6.0 Q resistorO the 3.0 N resistorEXERCISEHINTS: GETTING STARTED| I'M STUCK!Suppose the series resistors in the example are now 4.00 and 2.00 2 while the parallel resistors are4.00 N (top) and 2.00 2 (bottom), and the battery provides an emf of 76.0 V.(a) Find the equivalent resistance.Reg(b) Find the currents I, I,, and I,.I =AAI2 =A

Answered: Image /qna-images/answer/3736ede2-a63b-46e1-89a4-b89541b7b86e.jpg

Suppose the series resistors in the example are now 4.00 N and 2.00 N while the parallel resistors are 4.00 N (top) and 2.00 N (bottom), and the battery provides an emf of 76.0 V. (a) Find the equivalent resistance. Ω R `eq (b) Find the currents I, I,, and I2. |A I2

Suppose the series resistors in the example are now 4.00 N and 2.00 N while the parallel resistors are 4.00 N (top) and 2.00 N (bottom), and the battery provides an emf of 76.0 V. (a) Find the equivalent resistance. Ω R `eq (b) Find the currents I, I,, and I2. |A I2

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter21: Current And Direct Current Circuits

Section: Chapter Questions

Problem 63P

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Question

SOLUTION
(a) Find the equivalent resistance of the circuit.
R = R, + R, = 8.0 2 + 4.0 2 = 12.0 0
eq
The 8.0-2 and 4.0-2 resistors are in
series, so use the sum rule to find the
equivalent resistance between a and b.
The 6.0-2 and 3.0-0 resistors are in
1
1
%3D
R
eq
6.0 2
2.0 Q
R,
Reg
parallel, so use the reciprocal-sum rule
R,
3.0 0
to find the equivalent resistance
= 2.0 2
between b and c (don't forget to
invert!).
In the new diagram, figure b, there are
R
-R, + R, -12.0 Ω+ 2.0 Ω-14.0 Ω
eq
now two resistors in series. Combine
them with the sum rule to find the
equivalent resistance of the circuit.
(b) Find the current in each resistor if a 42-V battery is connected between points a and c.
Δν
I =
Find the current in the equivalent
42 V
= 3.0 A
ac =
R
eq
resistor in figure c, which is the total
14 2
current. Resistors in series all carry the
same current, so the value is the
current in the 12-2 resistor in figure b
and also in the 8.0-N and 4.0-2
resistors in figure a.
Calculate the voltage drop AV
para
Δν
para
= IR = (3.0 A)(2.0 2) = 6.0 V
across the parallel circuit, which has an
equivalent resistance of 2.0 Q.
Apply Ohm's law again to find the
Δν
para
6.0 V
= 1.0 A
currents in each resistor of the parallel
6.0 2
R6,0 0
circuit.
Δν
para
6.0 V
I2
= 2.0 A
3.0 2
R3,0 0
LEARN MORE
REMARKS As a final check, note that AV = (6.0 2)I, = (3.0 N)I, = 6.0 V and
bc
AVh = (12 N)I, = 36 V; therefore, AV
= AV + AV = 42 V, as expected.
bc
ас
ab
QUESTION Which of the original resistors dissipates energy at the greatest rate?
O the 8.0 2 resistor
O the 4.0 2 resistor
O the 6.0 Q resistor
O the 3.0 N resistor
EXERCISE
HINTS: GETTING STARTED
| I'M STUCK!
Suppose the series resistors in the example are now 4.00 and 2.00 2 while the parallel resistors are
4.00 N (top) and 2.00 2 (bottom), and the battery provides an emf of 76.0 V.
(a) Find the equivalent resistance.
Reg
(b) Find the currents I, I,, and I,.
I =
A
A
I2 =
A

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