For the circuit shown in Figure P21.50, 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 P21.50
(a)
The equations for the upper loop in the circuit diagram.
Answer to Problem 50P
The equation for the upper loop is
Explanation of Solution
Write the expression for the Kirchhoff’s loop rule for the upper loop going counter clockwise.
Conclusion:
Therefore, the equation for the upper loop is
(b)
The equations for the lower loop in the circuit diagram.
Answer to Problem 50P
The equation for the lower loop is
Explanation of Solution
Write the expression for the Kirchhoff’s loop rule for the lower loop going counter clockwise.
Conclusion:
Therefore, the equation for the lower loop is
(c)
The equation of the junction on the left side in the circuit diagram.
Answer to Problem 50P
The equation of the junction in the left side is
Explanation of Solution
Write the expression for the Kirchhoff’s junction rule for the junction on the left side in the circuit.
Conclusion:
Therefore, the equation of the junction in the left side is
(d)
The equation for
Answer to Problem 50P
The equation for
Explanation of Solution
Use equation (III) to solve for
Conclusion:
Therefore, the equation for
(e)
The equation of the lower loop without using
Answer to Problem 50P
The equation of the lower loop without using
Explanation of Solution
Use equation (IV) in (II) to solve for the lower without using
Conclusion:
Therefore, the equation of the lower loop without using
(f)
The value of current
Answer to Problem 50P
The value of current
Explanation of Solution
Use equation (V) to solve for
Use equation (VI) in (I) to solve for
Use equation (VII) in (I) to solve for
Conclusion:
Therefore, the value of current
(g)
The value of current
Answer to Problem 50P
The value of current
Explanation of Solution
Use equation (VIII) and (VII) in (IV) to solve for
Conclusion:
Therefore, the value of current
(h)
The significance of negative sign in the current
Answer to Problem 50P
The negative sign for
Explanation of Solution
The negative sign in the value of the current
Conclusion:
Therefore, the negative sign for
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Chapter 21 Solutions
Principles of Physics
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