PHY127 Final Exam A
Problem 1 (6+6+6+6+6)
A rectangular coil with resistance
R has N turns, each length l and
width w as in Fig. The coil moves
with constant velocity into a uniform
magnetic field B with a gap d in the
middle. Answer the following
questions (Use N,B, l, v, R, L, w, and d as
needed). Assume d< l < L. The magnetic field goes
into the paper perpendicularly.
What are the magnitude and direction of the total
magnetic force on the coil and the direction of
the current (clockwise, counter clockwise or zero)
when the right segment of the coil is at x (see Fig.):
(a) 0 ≤ x < l
l≤x<L
(c) L ≤ x < L + d
(b)
L+d ≤ x < L+l
(e) 2 L + d + l ≤ x
(d)
L
d
L
x
x=0
Problem 2 (10+10+10 points)
Mike is designing a radio receiver using a RLC series circuit to listen to his
favorite FM radio stations at the frequencies between 86 MHz and 102 MHz.
In the circuit radio waves induce current that depends on the values of R, L, C
and the frequencies of the waves. For this purpose he purchased at a Radio
Shack store, a coil with inductance L of 6.0 µH, a resistor with resistance R
of 25 Ω, and a variable capacitor that can change the capacitance C.
(a) Find the range of the capacitance C the variable capacitor should cover to
tune to all his favorite stations. Explain the reasoning of your calculation too.
(b) When the receiver is tuned to receive radio waves from a FM station at
the frequency of 86 MHz, the rms voltage difference ∆Vrms(86 MHz) across
the resistor is 500 mV. What are the value of the Irms and the average power
delivered to the resistor Pav?
(c) When the receiver is tuned at 86 MHz, what are the average power delivered
Pav to the resistor and the rms voltage difference ∆Vrms across the resistor for
the radio waves that induce only the half of the Irms for the frequency of 86
MHz?
Problem 3 (7+7+6+10 points)
(a) Apply Kirchhoff’s rules to the loop
fabef and write an equation using
i1 and i as two unknown currents
(7 points).
(b) Apply Kirchhoff’s rules to the loop
bcdeb and write an equation using
i1 and i2 as two unknown currents
f
(7 points).
(c) Express the current i in terms of i1 and i2 (6 points).
c
e
d
(d) Using the equations obtained in part (a),(b) and (c), find numerical values for
i, i1 and i2 (10 points)