Consider the circuit shown below. (b) ww (c) 8.0 92 wwww 4.0 92 www E2= 5.0 V HH 5.0 Ω www &1= 9.0 V To ensure uniformity in notation and signs, designate the currents in the three branches as follows. Call the current in the left branch 1₁, the current in the center branch 1₂, and the current in the right branch I3. Assume the direction of I, is upward, the direction of I₂ is upward, and the direction of I, is downward. (a) 10.0 92 Apply the junction rule at the top junction (between the 8-9 and 5-2 resistors) to obtain a relation between 1₁, 1₂, and 13. Apply the loop rule to the left loop (containing I, and I₂) and to the right loop (containing I₂ and 13). Start at the top junction (between the 8-92 and 5-9 resistors), and traverse each loop in the counterclockwise direction. You may omit the units for convenience. Solve the system of three equations (obtained in parts (a) and (b)) for 1₁, 1₂, and 13. (Include the sign for each current.)

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Chapter1: Units, Trigonometry. And Vectors
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Consider the circuit shown below.
(b)
8.0 Ω
www
(c)
4.0 92
8₁ 9.0 V
82= 5.0 V
5.0 Ω
ww
To ensure uniformity in notation and signs, designate the currents in the three branches as
follows. Call the current in the left branch 1₁, the current in the center branch 1₂, and the current
in the right branch 13. Assume the direction of I, is upward, the direction of I₂ is upward, and
the direction of 13 is downward.
(a)
10.0 Ω
Apply the junction rule at the top junction (between the 8-22 and 5-2 resistors) to obtain
a relation between I₁, I2, and 13.
2
Apply the loop rule to the left loop (containing I, and I₂) and to the right loop
(containing I₂ and 13). Start at the top junction (between the 8-92 and 5-2 resistors), and
traverse each loop in the counterclockwise direction. You may omit the units for
convenience.
Solve the system of three equations (obtained in parts (a) and (b)) for I₁, I2, and 13.
(Include the sign for each current.)
Transcribed Image Text:Consider the circuit shown below. (b) 8.0 Ω www (c) 4.0 92 8₁ 9.0 V 82= 5.0 V 5.0 Ω ww To ensure uniformity in notation and signs, designate the currents in the three branches as follows. Call the current in the left branch 1₁, the current in the center branch 1₂, and the current in the right branch 13. Assume the direction of I, is upward, the direction of I₂ is upward, and the direction of 13 is downward. (a) 10.0 Ω Apply the junction rule at the top junction (between the 8-22 and 5-2 resistors) to obtain a relation between I₁, I2, and 13. 2 Apply the loop rule to the left loop (containing I, and I₂) and to the right loop (containing I₂ and 13). Start at the top junction (between the 8-92 and 5-2 resistors), and traverse each loop in the counterclockwise direction. You may omit the units for convenience. Solve the system of three equations (obtained in parts (a) and (b)) for I₁, I2, and 13. (Include the sign for each current.)
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