Physics 2114
Midterm Exam 3
Professor Bandy
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Fall 2014
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Problem 1 Two Parts: See Fig. 1 Coordinate system is given. Answer a – h.
Part 1. An AC generator with maximum voltage of 120.0 V and a frequency of
6.0 Hz is connected to a resistor R = 20 . The switch S is connected to A so the
circuit bypasses the capacitor. Answer a – e.
a. Calculate the rms voltage across resistor.
(32)
R=20 
S
A
B
C=1000 F
V
V
ĵ
b. Show the frequency 𝜔 of the source is 37.7 [𝑠
−1
, 𝑑𝑦𝑛𝑒, 𝑟𝑎𝑑𝑖𝑎𝑛 ∙ 𝑠
Circle Correct Unit
−1
].
Figure 1
Ideal Voltmeter
k̂
iˆ
c. Calculate the instantaneous resistor voltage at t = 1.2s.
d. Calculate the peak current in the circuit.
e. If the frequency of the generator is increased, the average power dissipated in the resistor
[increases, decreases, stays the same]. In the phasor diagram the current [leads, lags, is in phase with] the voltage.
Circle One
Circle One
Part 2. Connect switch to B so that the circuit now includes the capacitor C=1000 F. The voltage is read from the ideal
voltmeter V across the capacitor. Answer f - h.
f. Calculate two items: the cross-over frequency c and show the capacitive reactance 𝜒𝑐 = 26.5 [ V, , A]
Calculate:
Circle Correct Unit
c
Calculate:
𝜒𝑐
g. Calculate the capacitor voltage at c.
h. This is a [low-, high-, square] pass filter that [blocks, transmits, squares] frequencies greater than c.
Circle One
Circle One
Physics 2114
Midterm Exam 3
Professor Bandy
Fall 2014
Problem 2 Two Parts: Answer questions a – f.
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Part 1: A 15.0-mW Helium-Neon laser emits a beam of circular cross section with a radius of 1.00 mm. Answer a - d.
a. Show the magnitude of the Poynting vector in the beam is 4.78 kW/m2.
b. Calculate the maximum electric field in the beam.
c. Show the total energy that is contained in a 1.00-m length of the beam is 5.0 × 10−11 [ W,
s,
J ].
Circle Correct Unit
d. Find the momentum that is carried by a 1.00-m length of the beam.
Part 2: An electron moves with velocity 𝑣⃗ = 10.0𝑖̂ 𝑚/𝑠 through a uniform electric field⃗⃗⃗⃗
𝐸 = (2.50𝑖̂ + 5.00 𝑗̂) V/m
̂
⃗⃗ = 0.400𝑘 𝑇. Answer e - f.
and a uniform magnetic field 𝐵
e. Calculate the force 𝐹⃗ on the electron.
f.
Calculate the acceleration 𝑎⃗ of the electron.
Physics 2114
Midterm Exam 3
Professor Bandy
Fall 2014
Problem 3 Two Parts: See Fig. 2. Answer a – h.
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Part 1: A 510-turn solenoid has a radius of 8.00 mm and an overall length of 14.0 cm. It is connected in series with
a 2.50- resistor and a 12-V battery. Switches S1 and S3 are open, switch S2 is closed. Answer a - c.
a. Independent of the circuit, show that the inductance of the solenoid is 0.469 mH.
b. Calculate the time constant of the circuit.
c. Calculate the time interval where the current will reach 50% of its final value.
L
S3
C
S2
R
S1
𝑒𝑚𝑓
Figure 2
C=9.0 pF, emf=12V,
R=2.5L=0.469 mH
Part 2: Switches S2 and S3 are open, switch S1 is closed for a long time so the capacitor can be fully charged. The
capacitance is 9.0 pF. Switch S3 is then closed, S1 and S2 are open, removing the battery, leaving only the inductor
and capacitor in series. Answer d – h.
d. Calculate the frequency f of oscillation of the circuit.
e. Show the maximum value of the charge on the capacitor is 1.08 × 10−10 𝐶.
f.
Calculate the maximum values of the current in the circuit.
g. The direction of the current is [cw, ccw, neither, both]. Explain.
Circle One
h. Verify or not if the capacitance can be 9.0 pF. Explain.