
Concept explainers
(a)
The expression for the current in the light bulb
(a)

Answer to Problem 56P
The expression for the current is
Explanation of Solution
Write the equation for the current in the bulb in term of the emf.
Here,
Here,
Conclusion:
Substitute equation (II) in equation (I).
Therefore, the expression for the current in the light bulb as a function of
(b)
The analysis model describing the moving bar
(b)

Answer to Problem 56P
The analysis model describing the moving when the bulb has maximum power is particle under equilibrium.
Explanation of Solution
Write the equation for the power of the light bulb.
Here,
From the above equation, both the force and the velocity of the moving have to be maximum for the power on the light bulb to be maximum. The condition of maximum power points to energy loss which could happen only for a particle in equilibrium.
Conclusion:
Therefore, the analysis model describing the moving when the bulb has maximum power is particle under equilibrium.
(c)
The speed of the bar
(c)

Answer to Problem 56P
The speed of the bar at maximum power is
Explanation of Solution
The magnetic flux points into the page thereby making the counterclockwise current to move out of the page. Write the equation for the magnetic force that the current is flowing upwards in the bar.
Here,
Conclusion:
Substitute
Therefore, the speed of the bar at maximum power is
(d)
The current in the bulb
(d)

Answer to Problem 56P
The current in the light bulb at maximum power is
Explanation of Solution
Substitute equation (V) in equation (III).
Conclusion:
Substitute
Therefore, the current in the light bulb at maximum power is
(e)
The maximum power delivered
(e)

Answer to Problem 56P
The maximum power delivered to the light bulb is
Explanation of Solution
Write the equation for the power in the light bulb.
Here,
Conclusion:
Substitute
Therefore, the maximum power delivered to the light bulb is
(f)
The maximum input power delivered
(f)

Answer to Problem 56P
The maximum input power delivered to the bar is
Explanation of Solution
Write the equation for the power delivered to the bar.
Here,
Conclusion:
Substitute
Therefore, the maximum input power delivered to the bar is
(g)
Whether the speed changes or not
(g)

Answer to Problem 56P
The speed changes when the resistance increases.
Explanation of Solution
Write the equation for the speed of the bar from equation (V).
Hence, the speed of the bar and the resistance are proportional to each other, given, all other quantities are kept constant.
Conclusion:
Therefore, the speed of the bar changes when the resistance increases.
(h)
Whether the speed increases or decreases
(h)

Answer to Problem 56P
The speed changes increases the resistance increases.
Explanation of Solution
Write the equation for the speed of the bar from equation (V).
Hence, the speed of the bar and the resistance are proportional to each other, given, all other quantities are kept constant.
Conclusion:
Therefore, the speed of the bar increases when the resistance increases.
(i)
Whether the power changes
(i)

Answer to Problem 56P
The power changes when the current increases
Explanation of Solution
An increase in current leads to a change in the mechanical load as the current as the current is analogous to mechanical load.
The mechanical power depends on the load. Therefore, the change in current will lead to change in the power.
Conclusion:
Therefore, the power changes when the current increases.
(j)
Whether the power is smaller or larger
(j)

Answer to Problem 56P
The power changes and becomes larger.
Explanation of Solution
According to ohm’s law, the current and resistance are inversely proportional to each other. If the current and resistance has to increase together, the load has to increase further.
The increase in the load will increase the power.
Conclusion:
Therefore, the power changes and becomes larger when the current and resistance increases.
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Chapter 23 Solutions
Principles of Physics: A Calculus-Based Text
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