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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- A Figure P32.74 shows an N-turn rectangular coil of length a and width b entering a region of uniform magnetic field of magnitude Bout directed out of the page. The velocity of the coil is constant and is upward in the figure. The total resistance of the coil is R. What are the magnitude and direction of the magnetic force on the coil a. when only a portion of the coil has entered the region with the field, b. when the coil is completely embedded in the field, and c. as the coil begins to exit the region with the field?arrow_forwardFigure P30.39 shows a stationary conductor whose shape is similar to the letter e. The radius of its circular portion is a = 50.0 cm. It is placed in a constant magnetic field of 0.500 T directed out of the page. A straight conducting rod, 50.0 cm long, is pivoted about point O and rotates with a constant angular speed of 2.00 rad/s. (a) Determine the induced emf in the loop POQ. Note that the area of the loop is a2/2. (b) If all the conducting material has a resistance per length of 5.00 /m, what is the induced current in the loop POQ at the instant 0.250 s after point P passes point Q? Figure P30.39arrow_forwardA metal rod of mass m slides without friction along two parallel horizontal rails, separated by a distance and connected by a resistor R, as shown in Figure P30.13. A uniform vertical magnetic field of magnitude B is applied perpendicular to the plane of the paper. The applied force shown in the figure acts only for a moment, to give the rod a speed v. In terms of m, , R, B, and v, find the distance the rod will then slide as it coasts to a stop. Figure P30.13arrow_forward
- A conducting rod of length = 35.0 cm is free to slide on two parallel conducting bars as shown in Figure P30.35. Two resistors R1 = 2.00 and R2 = 5.00 are connected across the ends of the bars to form a loop. A constant magnetic field B = 2.50 T is directed perpendicularly into the page. An external agent pulls the rod to the left with a constant speed of v = 8.00 m/s. Find (a) the currents in both resistors, (b) the total power delivered to the resistance of the circuit, and (c) the magnitude of the applied force that is needed to move the rod with this constant velocity. Figure P30.35arrow_forwardA long, straight wire carries a current given by I = Imax sin (t + ). The wire lies in the plane of a rectangular coil of N turns of wire as shown in Figure P30.45. The quantities Imax, , and are all constants. Assume Imax = 50.0 A, = 200 s1, N = 100, h = = 5.00 cm, and L = 20.0 cm. Determine the emf induced in the coil by the magnetic field created by the current in the straight wire. Figure P30.45arrow_forwardWhy is the following situation impossible? A conducting rectangular loop of mass M = 0.100 kg, resistance R = 1.00 , and dimensions w = 50.0 cm by = 90.0 cm is held with its lower edge just above a region with a uniform magnetic field of magnitude B = 1.00 T as shown in Figure P30.34. The loop is released from rest. Just as the top edge of the loop reaches the region containing the field, the loop moves with a speed 4.00 m/s. Figure P30.34arrow_forward
- Consider the apparatus shown in Figure P30.32: a conducting bar is moved along two rails connected to an incandescent lightbulb. The whole system is immersed in a magnetic field of magnitude B = 0.400 T perpendicular and into the page. The distance between the horizontal rails is = 0.800 m. The resistance of the lightbulb is R = 48.0 , assumed to be constant. The bar and rails have negligible resistance. The bar is moved toward the right by a constant force of magnitude F = 0.600 N. We wish to find the maximum power delivered to the lightbulb. (a) Find an expression for the current in the lightbulb as a function of B, , R, and v, the speed of the bar. (b) When the maximum power is delivered to the lightbulb, what analysis model properly describes the moving bar? (c) Use the analysis model in part (b) to find a numerical value for the speed v of the bar when the maximum power is being delivered to the lightbulb. (d) Find the current in the lightbulb when maximum power is being delivered to it. (e) Using P = I2R, what is the maximum power delivered to the lightbulb? (f) What is the maximum mechanical input power delivered to the bar by the force F? (g) We have assumed the resistance of the lightbulb is constant. In reality, as the power delivered to the lightbulb increases, the filament temperature increases and the resistance increases. Does the speed found in part (c) change if the resistance increases and all other quantities are held constant? (h) If so, does the speed found in part (c) increase or decrease? If not, explain. (i) With the assumption that the resistance of the lightbulb increases as the current increases, does the power found in part (f) change? (j) If so, is the power found in part (f) larger or smaller? If not, explain. Figure P30.32arrow_forwardA circular loop of wire with a radius of 4.0 cm is in a uniform magnetic field of magnitude 0.060 T. The plane of the loop is perpendicular to the direction of the magnetic field. In a time interval of 0.50 s, the magnetic field changes to the opposite direction with a magnitude of 0.040 T. What is the magnitude of the average emf induced in the loop? (a) 0.20 V (b) 0.025 V (c) 5.0 mV (d) 1.0 mV (e) 0.20 mVarrow_forwardFigure P32.21 shows a circular conducting loop with a 5.00-cm radius and a total resistance of 1.30 placed within a uniform magnetic field pointing into the page. a. What is the rate at which the magnetic field is changing if a counterclockwise current I = 4.60 102 A is induced in the loop? b. Is the induced current caused by an increase or a decrease in the magnetic field with time?arrow_forward
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