Homework #11 203-1-1721 Physics... 2. A circular coil has a 10.3 cm radius... externally produced magnetic field of 2.62 mT is perpendicular to...

Homework #11 203-1-1721 Physics... 2. A circular coil has a 10.3 cm radius... externally produced magnetic field of 2.62 mT is perpendicular to...

Homework #11
203-1-1721
Physics 2 for Students of Mechanical Engineering
2. A circular coil has a 10.3 cm radius and consists of 34 closely wound turns of wire. An
externally produced magnetic field of 2.62 mT is perpendicular to the coil. (a) If no
current is in the coil, what is the number of flux linkages, NΦB, for the solenoid. (b)
When the current in the coil is 3.77 A in a certain direction, the net flux through the coil
is found to vanish. Find the inductance of the coil.
5.
The inductance of a closely wound N-turn coil is such that an emf of 3.0 mV is induced
when the current changes at the rate of 5.0 A/s. A steady state current of 8.0 A produces
a magnetic flux of 40 µWb through each turn. (a) Calculate the inductance of the coil.
(b) How many turns does the coil have?
6.
A toroid having a 5.20 cm square cross-section and an inside radius of 15.3 cm has 536
turns of wire and carries a current of 810 mA. Calculate the magnetic flux through a
cross-section.
8.
The current i through a 4.6 H inductor varies with time t as shown on the graph of Fig.
36-18 below. Calculate the induced emf during the time intervals (a) t = 0 to t =2 ms,
(b) t = 2 ms to t = 5 ms, and (c) t = 5 ms to t = 6 ms. (Ignore the behavior at the ends of
each interval.)
12. Consider the LR circuit of Fig. 36-4 below. (a) In terms of the battery emf ε, what is the
induced emf εL when the switch has just been closed on a? (b) What is εL after two time
constants? (c) After how many time constants will εL bee just one-half of the battery
emf ε?
15. Suppose the emf of the battery in the circuit of Fig. 36-4 above (with the switch closed
on a) varies with time to so that current is given by i(t) = (3.0 A) + (5.0 A/s)t. Take R =
4.0 Ω, L = 6.0 H, and find an expression for the battery emf as a function of time. (Hint:
Apply the loop rule.)
19. In Fig. 36-19 below, ε = 100 V, R1 = 10 Ω, R2 = 20 Ω, R3 = 30 Ω, and L = 2.0 H. Find
the values of i1 and i2 (a) immediately after switch S is closed, (b) a long time later, (c)
immediately after switch S is opened again, and (d) a long time later.
21. In the circuit shown in Fig. 36-20 below, ε = 10 V, R1 = 5 Ω, R2 = 10 Ω, and L = 5.0 H.
For the two separate conditions (I) switch S just closed and (II) switch S closed for a
long time, calculate (a) the current i1 through R1, (b) the current i2 through R2, (c) the
current i through the switch, (d) the potential difference across R2, (e) the potential
difference across L, and (f) di2/dt.
24. A solenoid 85.3 cm long has a cross-sectional area of 17.2 cm2. There are 950 turns of
wire carrying a current of 6.57 A. (a) Calculate the magnetic field energy density inside
the solenoid. (b) Find the total energy stored in the magnetic field inside the solenoid.
(Neglect effects near the ends of the solenoid.)
29. A coil is connected in series with a 10.4 kΩ resistor. When a 55.0 V battery is applied to
the two elements, the current reaches a value of 1.96 mA after 5.20 ms. (a) Find the
inductance of the coil. (b) How much energy is stored in the coil at this same moment?
30. For the circuit of Fig. 36-4 above, assume that ε = 12.2 V, R = 7.34 Ω, and L = 5.48 H.
The battery is connected at time t = 0. (a) How much energy is delivered by the battery
during the first 2.0 s? (b) How much of this energy is stored in the magnetic field of the
inductor? (c) How much energy has been dissipated as heat in the resistor?
42. An oscillating LC circuit consisting of a 1.13 nF capacitor and a 3.17 mH coil has a
peak potential drop of 2.87 V. Find (a) the maximum charge on the capacitor, (b) the
peak current in the circuit, and (c) the maximum energy stored in the magnetic field of
the coil.
44. In the circuit shown in Fig. 36-22 below, the switch has been in position a for a very
long time before it is thrown to position b. (a) Calculate the frequency of the resulting
oscillating current. (b) What will be the amplitude of the current oscillations?
45. An LC circuit has an inductance of 3.0 mH and a capacitance of 10 µF. Calculate (a) the
angular frequency and (b) the period of oscillation. (c) At time t = 0 the capacitor is
charged to 200 µC, and the current is zero. Sketch roughly the charge on the capacitor
as a function of time.
52. A single loop circuit consists of a 7.22 Ω resistor, a 12.3 H inductor, and a 3.18 µF
capacitor. Initially, the capacitor has a charge of 6.31 µC and the current is zero.
Calculate the charge on the capacitor N complete cycles later for N = 5, 10, and 100.
54. How much resistance R should be connected to an inductor L = 220 mH and capacitor C
= 12 µF in series in order that the maximum charge on the capacitor decays to 99% of
its initial value in 50 cycles?