For the circuit shown in Figure P27.22, we wish to find the currents I1, I2, and I3. Use Kirchhoff’s rules to obtain equations for (a) the upper loop, (b) the lower loop, and (c) the junction on the left side. In each case, suppress units for clarity and simplify, combining the terms. (d) Solve the junction equation for I3. (e) Using the equation found in part (d), eliminate I3 from the equation found in part (b). (f) Solve the equations found in parts (a) and (e) simultaneously for the two unknowns I1 and I2. (g) Substitute the answers found in part (f) into the junction equation found in part (d), solving for I3. (h) What is the significance of the negative answer for I2?
Figure P27.22
(a)
Answer to Problem 28.34P
Explanation of Solution
Given info: The figure is given as,
By going counterclockwise around the upper loop and suppressing the unites, the Kirchhoff’s law is applied.
The equation for the upper loop is,
Conclusion:
Therefore, the equation by using Kirchhoff’s rules in the upper loop is
(b)
Answer to Problem 28.34P
Explanation of Solution
Given info: The figure is given as,
By going counterclockwise around the lower loop and suppressing the unites, the Kirchhoff’s law is applied.
The equation for the lower loop is,
Conclusion:
Therefore, the equation by using Kirchhoff’s rules in the lower loop is
(c)
Answer to Problem 28.34P
Explanation of Solution
Given info: The figure is given as,
Apply the junction rule at the node in the left end of the circuit.
The equation for the junction on the left side is,
Conclusion:
Therefore, the equation by using Kirchhoff’s rules at the junction on the left side is
(d)
To solve: The junction on the left side for
Answer to Problem 28.34P
Explanation of Solution
Given info: The figure is given as,
Apply the junction rule at the node in the left end of the circuit.
Rearrange the equation (3) as,
Conclusion:
Therefore, the junction on the left side for
(e)
To eliminate: The current
Answer to Problem 28.34P
Explanation of Solution
Given info: The figure is given as,
The equation for
Substitute
Conclusion:
Therefore, the equation after elimination for
(f)
Answer to Problem 28.34P
Explanation of Solution
Given info: The figure is given as,
Rearrange the equation (4) for
Recall the equation (1).
Substitute
Further, solve,
Thus, the value of
Substitute
Conclusion:
Therefore, the value of
(g)
Answer to Problem 28.34P
Explanation of Solution
Given info: The figure is given as,
The equation for
Substitute
Conclusion:
Therefore, the value of
(h)
Answer to Problem 28.34P
Explanation of Solution
Given info: The figure is given as,
The negative sign in the answer for
Conclusion:
Therefore, the negative sign in the answer for
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Chapter 28 Solutions
Physics For Scientists And Engineers, Technology Update, Loose-leaf Version
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