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)
The equation by using Kirchhoff’s rules in the upper loop.
Answer to Problem 22P
The equation by using Kirchhoff’s rules in the upper loop is
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)
The equation by using Kirchhoff’s rules in the lower loop.
Answer to Problem 22P
The equation by using Kirchhoff’s rules in the lower loop is
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)
The equation by using Kirchhoff’s rules at the junction on the left side.
Answer to Problem 22P
The equation by using Kirchhoff’s rules at the junction on the left side is
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 22P
The junction on the left side for
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 22P
The equation after elimination\ for
Explanation of Solution
Given info: The figure is given as,
The equation for
Substitute
Conclusion:
Therefore, the equation after elimination for
(f)
The value of
Answer to Problem 22P
The value of
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)
The value of
Answer to Problem 22P
The value of
Explanation of Solution
Given info: The figure is given as,
The equation for
Substitute
Conclusion:
Therefore, the value of
(h)
The significant of the negative sign of answer of
Answer to Problem 22P
The negative sign in the answer for
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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