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college physics reasoning

Questions and Answers of College Physics Reasoning

Find the reactance of an inductor with L = 15 mH at 22 kHz. If the frequency is increased to 66 kHz, by what factor does the reactance change?
An inductor has a reactance of 5500Ω at a frequency of 2500 Hz. What is the value of L?
You are given two inductors with inductances of 40 μH and 80 mH. If the frequency is 5000 Hz, which inductor has the larger reactance?
In an AC circuit, does the voltage across an inductor differ in phase from the current by a phase angle of (a) zero,(b) 30°,(c) 45°,(d) 90°,(e) 180°
The phase angle between the voltage and current in an AC circuit is 90°. Is the average power delivered to the circuit from the AC source positive, negative, or zero?
Two capacitors with C1 = 4.5 mF and C2 = 1.9 mF are connected in series. What is the reactance of the equivalent capacitance at 350 Hz?
Two capacitors with C1 = 450 pF and C2= 820 pF are connected in parallel. What is the reactance of the equivalent capacitance at 30 kHz?
Consider a circuit containing a resistor with R = 1200Ω and a capacitor with C = 6.5μF. At what frequency does the reactance of the capacitor equal the resistance of the resistor?
Two capacitors are connected to an AC source as shown in Figure P22.27; assume VAC = Vmax = sin(2μft), with Vmax = 18 V and a frequency f 2000 Hz. (a) What is the amplitude (peak value) of the
For the circuit in Figure P22.20, find(a) the average power,(b) the maximum instantaneous power,(c) the minimum instantaneous power delivered to the capacitor. Use f 400 Hz, Vmax = 25 V, and C = 1.5
Consider the AC circuit in Figure P22.20 and assume VAC = Vmax sin(2πft) with Vmax = 12 V, f = 300 Hz, and C = 1.5μF. The charge on the capacitor will also vary sinusoidally. Find(a) the amplitude
The AC voltage across a capacitor with C = 1.5μF has an amplitude of Vmax = 22 V, and the current through the capacitor has an amplitude of 2.5 mA. What is the frequency?
A capacitor has a reactance of 450Ω at 1200 Hz. What is its capacitance?
If the frequency is increased from 35 Hz to 140 Hz, does the reactance of a capacitor increase or decrease? By what factor does it change?
What is the reactance of a 1200-pF capacitor at 400 Hz?
An AC voltage source with a frequency of 120 Hz and an amplitude Vmax = 25 V is connected across a capacitor with C = 1.5μF (Fig. P22.20). Draw a phasor diagram showing the voltage across and
You are given two capacitors with capacitances of 20 pF and 20 μF. If the frequency is 5000 Hz, which capacitor has the larger reactance?
In an AC circuit, does the voltage across a capacitor differ in phase from the current by a phase angle of (a) zero,(b) 30°,(c) 45°,(d) 90°,(e) 180°
Consider the circuit in Figure P22.16 and suppose R1 = 20Ω and R2 = 40Ω. If the total average power dissipated in the two resistors is 55 W, what is the amplitude Vmax of the AC voltage?
Make a phasor diagram for the circuit in Figure P22.16 showing the voltage across each resistor and the current through each resistor. Do these phasors make the same angle with the horizontal axis?
Make a phasor diagram for the circuit considered in Problem 14, showing the voltage across each resistor and the current through the circuit. Do these three phasors all make the same angle with the
Consider the AC circuit containing two resistors in Figure P22.14. If the amplitude of the AC voltage source is Vmax = 25 V, R1= 300Ω and R2 = 500Ω what is the amplitude of the
A heater runs on an AC voltage of 120 V and draws a power of 25 W. If this heater were run instead on a DC voltage of 75 V, how much current would flow through the heater? The heater can be modeled
What is the resistance of a lightbulb that has a rating of 300 W? Assume the lightbulb is designed for use in an AC circuit with Vrms = 120 V. For simplicity, treat the lightbulb as a resistor whose
The average power dissipated in a 45-kΩ resistor in an AC circuit is 75 W. What is the amplitude of the AC voltage across the resistor?
The value of R for the resistor in Problem 9 is increased by a factor of 2.5 while the current is kept fixed. By what factor does the average power change?
A resistor with R 2.0 kΩ is connected to an AC generator that operates at 60 Hz with an amplitude of 35 V. Find(a) the amplitude of the current through the resistor,(b) the maximum
In an AC circuit, does the voltage across a resistor differ in phase from the current by a phase angle of (a) zero,(b) 30°,(c) 45°,(d) 90°,(e) 180°?
Consider an AC voltage source that produces a voltage given by V = Vmax = sin(2πft), with Vmax = 18 V and f = 6.2 Hz. What is the instantaneous value of the voltage at t = 1.4 s?
Consider the square wave voltage in Figure Q22.8. What is its frequency?
Suppose the loop in the generator in Figure Q22.6 is square and the length of each side of the loop is increased by a factor of two. By what factor will the AC voltage change?
Suppose the magnetic field B in the generator in Figure Q22.6 is reduced in magnitude by a factor of three. By what factor will the AC voltage change?(a) The voltage increases by a factor of
Make a graph of an AC voltage versus time that corresponds to a frequency of 300 Hz and an rms value of 45 V. Be sure to label the axes of your graph.
Some clocks that are powered by an AC voltage use the AC frequency to keep time. The power company makes this possible by arranging to have precisely the correct number of cycles that occur every
Figure P22.1 shows the AC voltage produced by a particular source. Estimate(a) the frequency of this voltage,(b) the amplitude of this voltage,(c) the rms value of this voltage.(d) If this AC voltage
When applying Kirchhoff’s loop rule to an AC circuit, one assumes the current in the loop is the same through all circuit elements at any particular instant. Changes in current travel at the speed
For an ideal generator, the electrical energy generated equals the work W done in making the shaft rotate. For a real generator, is the electrical energy greater than, equal to, or less than W?
Some resistors are made from a coil of wire. What is the best way to model the circuit behavior of such a resistor? Choose one answer and explain.(a) As an ideal resistor in series with an ideal
Sometimes an electrical device may need an input voltage that is a few percent higher or lower than the supply voltage. A boosting transformer connects the output coil with the input voltage (here, a
Although transformers are AC devices, is there some way to test a transformer to see if it works with a battery? Explain.
In actual transformers (Fig. Q22.19), the iron cores are actually comprised of thin sheets of metal laminated together with insulating layers in between. Why would the cores be made this way?Figure
How is a phasor different from a vector? Is the emf a vector quantity?
An LCR circuit with a resonant frequency of 40 Hz is connected to a standard U.S. wall outlet of 120 V AC. Does the current in the circuit “lag” or “lead” the emf? That is, does the current
The equations describing an LC oscillator are very similar in form to those describing the mechanical harmonic oscillator of a mass on a spring. Identify the term in the equation for the mechanical
An LC circuit is called an oscillator. What, physically, is oscillating in such a circuit? What variables are periodic?
A capacitor is connected in parallel with an inductor, and this circuit is connected to an AC voltage source of frequency f. It is found that the impedance of this circuit increases if the frequency
Consider the circuit in Figure Q22.13.(a) Draw equivalent circuits that apply at high and low frequencies.(b) Estimate the ratio Vout/Vin at high and low frequencies.(c) Explain how this circuit acts
The reactance of an inductor is given by XL = 2pfL. Show that this reactance has units of ohms. Explain why it makes sense to compare the reactance of an inductor with the resistance of a resistor.
Show that the reactance XC of a capacitor has units of ohms. Explain why it makes sense to compare the reactance of a capacitor with the resistance of a resistor.
If the voltage across a capacitor is V = Vmax sin(2πft), the charge on the capacitor is also proportional to sin(2πft) (see Eq. 22.17). The current through the capacitor in this case is given by I
Consider two AC voltage sources connected in series with voltages V1 = V1, max sin(2πft) and V2 = V2, max sin(2πft p/4), and V1, max V2, max 30 V. Show that these two sources in
Most AC voltage sources produce a voltage that varies sinusoidally with time, but some produce a “square wave” as sketched in Figure Q22.8. Use the general definition of rms voltage to find the
Discuss why it is relatively easy to change the amplitude of an AC voltage to a higher or lower value, but why it is difficult to change its frequency.
The AC generator described in Figure Q22.6 (and in Section 22.1) uses a rotating coil to produce an AC voltage through electromagnetic induction as described by Faraday’s law.(a) Explain how this
An AC source with a frequency of 60 Hz is connected to a lightbulb. The instantaneous brightness of the lightbulb depends on the magnitude of the instantaneous current. Explain why the brightness of
Figure Q22.4 shows an AC voltage source connected to a resistor in series with an unknown circuit element hidden in a box. The box might contain a single resistor, a single capacitor, or a single
A resistor is connected in series with an inductor (Fig. Q22.3). If the frequency of the AC voltage source is increased while its amplitude Vmax is kept fixed, does the current amplitude increase,
An AC circuit contains a capacitor in series with a resistor. If the frequency of the voltage source is increased while its amplitude is held fixed, does the current amplitude increase, decrease, or
Explain in words why(a) the reactance of a capacitor decreases as the frequency increases(b) the reactance of an inductor increases as the frequency increases.
Some cars, such as the Toyota Prius, have what are called regenerative brakes. In these braking systems, the kinetic energy of the car is stored in some fashion as the car is brought to a stop. That
The Earth’s magnetic field is approximately 5x10–5 T. Suppose a square coil of edge length 0.10 m is rotated with frequency f = 400 Hz about an axis perpendicular to the Earth’s field (Fig.
An inductor (L = 50 μH) is subjected to a time-varying current. The emf then produced by the inductor is graphed in Figure P21.70. The initial current is 40 mA. Plot the corresponding current as a
An inductor (L = 80 mH) is subjected to a time- varying current according to the graph in Figure P21.69. Plot the corresponding emf as a function of time. What is the highest potential
The circuit in Figure P21.68 has two identical resistors and three identical inductors. If L = 30 mH, what value must R have to give a time constant of 50 ms? ll ele Figure P21.68
The switch in Figure P21.67 is closed, and 5.5 μs later the current is measured to be 0.10 A.(a) What is the inductance L?(b) What is the maximum current in this circuit?(c) When is the current half
Consider an RL circuit with resistance 100Ω and inductance 200 mH.(a) If the battery is removed from the circuit and replaced by a connecting wire to complete the circuit, how long would it take
Consider an RL circuit with resistance 45Ω and inductance 250 mH placed in series.(a) If a 10-V battery is connected to the circuit, how long would it take the current to reach 10 mA?(b) What is
The switch in the circuit shown in Figure P21.64 has been open for a long time. The resistors in the circuit each have a value of 50Ω, the inductors each have a value of 40 mH, and V = 12 V.(a)
The 3.0-V flashlight bulb and wire loop assembly of Problem 62 is now attached to a wooden dowel with a crank handle as shown in Figure P21.63, and the loop is rotated in a uniform magnetic field of
A 3.0-V flashlight bulb is connected to a square loop of wire that measures 60 cm on a side as shown in Figure P21.62. Assume the bulb will only light if the potential across its terminals is at
Figure P21.61 shows four configurations of a wire loop placed near a long, straight wire with a time-varying current. Determine the direction of(a) the induced magnetic field in the wire loop (into
A loop of wire (loop 1) lies in a horizontal plane. A second loop (loop 2) of the same size is positioned above loop 1 and is also oriented horizontally (Fig. P21.60). The current in loop 1 is
A long, straight wire carrying a current I is next to a wire loop, with the straight wire lying in the plane of the loop (Fig. P21.59). The current I is increasing with time. What is the direction of
A loop of wire is placed in a magnetic field that varies with time according to the graph in Figure P21.58. Assume the loop is oriented perpendicular to the magnetic field. Sketch the graph for the
A loop of wire is placed in a time-varying magnetic fi eld B, inducing an emf in the loop whose magnitude varies with time as sketched in Figure P21.57 (top). Which of the graphs below shows how B
A battery of emf V is connected in series with a resistor of resistance R and an inductor with inductance L and number of turns N as sketched in Figure P21.56. After the current has been fl owing for
In Section 21.8, we mentioned that an emf is induced in a distant coil or current loop via an electromagnetic wave. For the case in Figure 21.32, this electromagnetic wave travels from the inner
A metal detector uses a coil to find pieces of metal that are buried or otherwise obscured. When a piece of metal is moved near a metal detector’s coil, an emf is induced in the coil. All else
A guitar string can vibrate at different frequencies, depending on how it is held (Chapter 12). Consider a string that is being played at either 400 Hz or 800 Hz. If everything else is kept the same,
The pickup coil in an electric guitar contains 10,000 turns and has a diameter of 2.0 mm. When the pickup coil is very close to a guitar string, there is a field of magnitude B = 0.10 T in the coil.
Use the result from Problem 50 to design a generator that produces an induced emf of 500 V. You must choose values for the number of loops and the area of each loop.
A single circular loop of wire of radius r = 2.0 cm rotates at a frequency of 60 Hz in a constant magnetic field of magnitude B = 1.5T. What is the approximate maximum emf induced in this generator?
Consider a region of space in which the energy density stored in the magnetic field (Eq. 21.35) is equal to the energy density in the electric field (Eq. 18.48). What is the ratio B/E? Express your
Consider again the circuit in Figure P21.42.(a) Suppose the switch is closed for a very long time. How much energy is stored in the inductor?(b) If the switch is then opened, where does this energy
Consider an MRI (magnetic resonance imaging) magnet that produces a magnetic field B = 1.5 T at a current I = 140 A. Assume the magnet is a solenoid with a radius of 0.30 m and a length of 2.0 m.(a)
What is the energy stored in the inductor in Figure P21.46 after the switch has been closed for a very long time? R = 1000 N V = 3.0 V L = 5.0 mH Figure P21.46
Consider two inductors L1 and L2 connected in parallel as shown in Figure P21.45. These two inductors act as one equivalent inductance Lequiv. To find Lequiv, we first notice that because they are
inductors act as one equivalent inductance Lequiv. To find Lequiv, we first note that because the current flows through the inductors sequentially, the factor ΔI/Δt is the same for each.(a) What is
Find the RL time constant for decay of the current in the circuit in Figure 21.25B. Express your answer in terms of the values of the resistances R1 and R2, and the inductance L. R2 R1
The switch in Figure P21.42 is open for a very long time and then closed at t = 0.(a) What is the current through R1 and through R2 immediately after the switch is closed?(b) What is the voltage
The switch in Figure P21.38 is open for a very long time and then closed at t = 0. What is the voltage across the resistor just after the switch is closed?Figure 21.38 ll
For the circuit in Figure P21.38, if R = 4000Ω, what must the value of L be to have a time constant of 1.5 s?Figure 21.38 ll
Consider again the circuit in Figure P21.38. The switch is first closed for a very long time so that the current through the inductor is constant. The switch is then opened suddenly. What is the
Consider an RL circuit (Fig. P21.38) with V = 9.0 V, L = 5.5 mH, and R 1500Ω. After the switch has been left open for a long time, the switch is closed at t = 0.(a) What is the current the instant
Figure P21.37 shows a top view of a mutual inductor (compare with Fig. 21.19). The two coils are shown in different colors, and the top and bottom wire leads are also indicated.(a) If the current in
The flux through an inductor with L = 5.0 mH changes at a rate of ΔΦB/Δt 0.0045 Tm2 /s. What is the rate of change ΔI/Δt of the current through the inductor?
An MRI magnet has an inductance of L = 5.0 H. What is the total flux through the magnet’s coils when the current is I = 100 A?
The number of turns in a solenoid is increased by a factor of three without changing the length.(a) By what factor does the magnetic field inside the solenoid change? (b) By what factor does the
An inductor has the form of a coil with 2000 turns and a diameter of 1.5 mm. The inductor is placed in a magnetic field perpendicular to the plane of the coil and increasing at a rate of 0.35 T/s.
An inductor with L = 1.5 mH is connected to a circuit that produces a current increasing steadily from 1.5 A to 5.6 A over a time of 2.3 s. What is the voltage across the inductor?

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