General Physics, 2nd Edition
General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
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Chapter 17, Problem 45E

(a)

To determine

The current through the 2ohm resistor.

(a)

Expert Solution
Check Mark

Answer to Problem 45E

The current through the 2ohm resistor is 1.5A_.

Explanation of Solution

The circuit is given in Figure 17.28.

Let us represent the 6ohm resistor as R1, the 3ohm resistor as R2, and the 2ohm resistor as R3.

R1 and R2 are connected parallel and R3 is in series to the combination of R1 and R2. Thus the equivalent resistance of the circuit can be obtained as,

  Req=R1,2+R3        (I)

Here, Req is the equivalent resistance, and R1,2 is the total resistance of the combination of R1 and R2.

Write the expression for total resistance of the combination of R1 and R2 which are connected in parallel.

  R1,2=R1R2R1+R2        (II)

Use equation (II) in (I).

  Req=R1R2R1+R2+R3        (III)

Since R3 is in series with the combination of R1 and R2, the current through R3 and the current through the combination of R1 and R2 will be same and is given by,

  I=VReq        (IV)

Here, I is the current, and V is the voltage difference across the whole circuit.

Conclusion:

Substitute 6ohm for R1, 3ohm for R2, and 2ohm for R3 in equation (III) to find Req.

  Req=(6ohm)(3ohm)(6ohm)+(3ohm)+(2ohm)=4ohm

Substitute 4ohm for Req, 6V for V in equation (IV) to find the current through the 2ohm resistor I.

  I=6V4ohm=1.5A

Therefore, the current through the 2ohm resistor is 1.5A_.

(b)

To determine

The voltage difference across the 3ohm resistor.

(b)

Expert Solution
Check Mark

Answer to Problem 45E

The voltage difference across the 3ohm resistor is 3V_.

Explanation of Solution

The current through the combination is 1.5A since it is same as that through R3. Since R1 and R2 are connected in parallel, the voltage difference across both of them will be same and is given by,

  V1,2=IR1,2        (V)

Here, V1,2 is the voltage across the combination of R1 and R2.

Use equation (II) in (V) and express V1,2 as V2 since the voltage difference is same for R1 and R2.

  V2=I(R1R2R1+R2)        (VI)

Conclusion:

Substitute 6ohm for R1, 3ohm for R2, and 1.5A for I in equation (VI) to find V2.

  V2=(1.5A)((6ohm)(3ohm)(6ohm)+(3ohm))=3V

Therefore, the voltage difference across the 3ohm resistor is 3V_.

(c)

To determine

The current through the 3ohm resistor.

(c)

Expert Solution
Check Mark

Answer to Problem 45E

The current through the 3ohm resistor is 1A_.

Explanation of Solution

It is obtained that the voltage across the 3ohm resistor is 3V.

Write the expression for the current through R2, the 3ohm resistor.

  I2=V2R2        (VII)

Conclusion:

Substitute 3V for V2, and 3ohm for R2 in equation (VII) to find I2.

  I2=3V3ohm=1A

Therefore, the current through the 3ohm resistor is 1A_.

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Chapter 17 Solutions

General Physics, 2nd Edition

Ch. 17 - Prob. 11RQCh. 17 - Prob. 12RQCh. 17 - Prob. 1ECh. 17 - Prob. 2ECh. 17 - Prob. 3ECh. 17 - Prob. 4ECh. 17 - Prob. 5ECh. 17 - Prob. 6ECh. 17 - Prob. 7ECh. 17 - Prob. 8ECh. 17 - Prob. 9ECh. 17 - Prob. 10ECh. 17 - Prob. 11ECh. 17 - Prob. 12ECh. 17 - Prob. 13ECh. 17 - Prob. 14ECh. 17 - Prob. 15ECh. 17 - Prob. 16ECh. 17 - Prob. 17ECh. 17 - Prob. 18ECh. 17 - Prob. 19ECh. 17 - Prob. 20ECh. 17 - Prob. 21ECh. 17 - Prob. 22ECh. 17 - Prob. 23ECh. 17 - Prob. 24ECh. 17 - Prob. 25ECh. 17 - Prob. 26ECh. 17 - Prob. 27ECh. 17 - Prob. 28ECh. 17 - Prob. 29ECh. 17 - Prob. 30ECh. 17 - Prob. 31ECh. 17 - Prob. 32ECh. 17 - Prob. 33ECh. 17 - Prob. 34ECh. 17 - Prob. 35ECh. 17 - Prob. 36ECh. 17 - Prob. 37ECh. 17 - Prob. 38ECh. 17 - Prob. 39ECh. 17 - Prob. 40ECh. 17 - Prob. 41ECh. 17 - Prob. 42ECh. 17 - Prob. 43ECh. 17 - Prob. 44ECh. 17 - Prob. 45ECh. 17 - Prob. 46ECh. 17 - Prob. 47ECh. 17 - Prob. 48ECh. 17 - Prob. 49ECh. 17 - Prob. 50ECh. 17 - Prob. 51ECh. 17 - Prob. 52ECh. 17 - Prob. 53ECh. 17 - Prob. 54ECh. 17 - Prob. 55ECh. 17 - Prob. 56ECh. 17 - Prob. 57ECh. 17 - Prob. 58ECh. 17 - Prob. 59ECh. 17 - Prob. 60ECh. 17 - Prob. 61ECh. 17 - Prob. 62ECh. 17 - Prob. 63ECh. 17 - Prob. 64ECh. 17 - Prob. 65ECh. 17 - Prob. 66ECh. 17 - Prob. 67ECh. 17 - Prob. 68ECh. 17 - Prob. 69ECh. 17 - Prob. 70ECh. 17 - Prob. 71ECh. 17 - Prob. 72ECh. 17 - Prob. 73ECh. 17 - Prob. 74ECh. 17 - Prob. 75ECh. 17 - Prob. 76ECh. 17 - Prob. 77ECh. 17 - Prob. 78ECh. 17 - Prob. 79ECh. 17 - Prob. 80ECh. 17 - Prob. 81ECh. 17 - Prob. 82ECh. 17 - Prob. 83ECh. 17 - Prob. 84ECh. 17 - Prob. 85ECh. 17 - Prob. 86ECh. 17 - Prob. 87ECh. 17 - Prob. 88ECh. 17 - Prob. 89ECh. 17 - Prob. 90ECh. 17 - Prob. 91ECh. 17 - Prob. 92E
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