(a)
The current in the
(a)
Answer to Problem 54AP
The current in
Explanation of Solution
Write the expression based on the junction rule.
Here,
Write the expression to obtain the loop rule.
Here,
Write the expression for the potential difference based on Ohm’s law.
Here,
The flow of current in the circuit is as shown in the figure below.
Figure-(1)
Here,
Write the equation of Kirchhoff’s voltage rule in the left loop.
Write the equation of Kirchhoff’s voltage rule in the right loop.
Conclusion:
Solve equation (I) and (II) to calculate
Therefore, the current in
(b)
The power delivered to the
(b)
Answer to Problem 54AP
The power delivered to the
Explanation of Solution
Write the expression to obtain the power across the
Here,
Conclusion:
Substitute
Therefore, the power delivered to the
(c)
The circuit in which Kirchhoff’s rule is required in find the value of current.
(c)
Answer to Problem 54AP
The Kirchhoff’s rule is required to find the value of current in case of circuit (c).
Explanation of Solution
In case of circuit (c), the current is flowing across each resistor and voltage drops at each resistor. As both the batteries of same emf are not in the same loop, thus, some amount of current will flow in the circuit. Hence, Kirchhoff’s rule is applicable in this case.
Conclusion:
In the case of the other two circuits, both the batteries of same emf are in the same loop. Thus they cancel out each other and no current flow in the circuit (b) and circuit (d).
Therefore, The Kirchhoff’s rule is required in find the value of current in case of circuit (c).
(d)
The circuit in which the smallest amount of power is delivered to the
(d)
Answer to Problem 54AP
The smallest power is delivered across the
Explanation of Solution
Conclusion:
The current flow diagram for circuit (b) is as shown in the figure below.
Figure-(2)
Write the equation of Kirchhoff’s voltage rule in right loop.
Write the expression based on junction rule.
Solve equation (III) and (IV) to calculate
Thus, the current across the circuit (b) is zero.
Therefore, the power delivered to across
The current flow diagram for circuit (c) is as shown in the figure below.
Figure-(3)
Write the equation of Kirchhoff’s voltage rule in the left loop.
Write the equation of Kirchhoff’s voltage rule in the left loop.
Solve equation (V) and (VI) to calculate
Write the expression to obtain the power across the
Here,
Substitute
Therefore, the power delivered to the
The current flow diagram for circuit (d) is as shown in the figure below.
Figure-(4)
Write the equation of Kirchhoff’s voltage rule in left loop.
Write the equation of Kirchhoff’s voltage rule in left loop.
Solve equation (VII) and (VIII) to calculate
Thus, the current across the circuit (d) is zero.
Therefore, the power delivered to across
Therefore the smallest power is delivered across
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Chapter 28 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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