HW # A
(1) Find the period of a periodic waveform with a frequency of 60 Hz
and 1000 Hz.
(2) Determine the angular velocity of a sine wave having a frequency of
60 Hz.
(3) Determine the frequency and period of the sine wave of Fig. 3.17(b).
(4) Given ω = 200 rad/s, determine how long it will take the sinusoidal
waveform to pass through an angle of 90°.
(5) Find the angle through which a sinusoidal waveform of 60 Hz will
pass in a period of 5 ms.
(6) Given e = 5 sin a, determine e at a = 40° and a = 0.8ω.
(7) Determine the angle at which the magnitude of the sinusoidal function
v = 10 sin 377t is 4 V.
(8) What is the phase relationship between the sinusoidal Waves for the
following voltage and current sets?
a. v = 10 sin (ωt + 30°) i = 5 sin (ωt - 70°)
b. i = 15 sin(ωt + 60°) v = 10 sin (ωt + 20°)
c. i = 2 cos (ωt + 10°) v = 3 sin (ωt + 10°)
d. i = sin (ωt + 30°)
v = 2 sin (ωt + 10°)
e. i = 2 cos (ωt + 60°) v = 3 sin (ωt + 150°)
(9) Find the effective value of the following sinusoidal waves:
a. v = 20 sin 754t
b. v = 7.07 sin 377t
c. i = 0.006 sin(400t + 20°)
d. i = 16 x10-3 sin(377t - 10°)
(10) Write the sinusoidal expressions for voltages and currents having
the following effective value at a frequency of 60 Hz with zero
phase shift:
a. 1.414 V b. 70.7 V
c. 0.06 A
d. 24 mA
(11) Determine the inductive reactance (in ohms) of a 2-H coil for the
following frequencies:
a. 25 Hz b. 60 Hz
c. 2000 Hz d. 100,000 Hz
(12) Determine the inductance of a coil that has a reactance of :
a. 20 Ω at f = 2 Hz.
b. 1000 Ω at f = 60 Hz.
c. 5280 Ω at f = 1000 Hz.
(13) Determine the frequency at which a 10-H inductance has the
following inductive reactances:
a. 50 Ω
b. 3770 Ω
c. 15.7 k Ω
d. 243 Ω
(14) The current through a 20 Ω inductive reactance is given. What is
the sinusoidal expression for the voltage?
a. i = 5 sin ωt
b. i = 0.4 sin(ωt + 60°)
c. i = 6 sin (ωt + 30°)
d. i = 3 cos (ωt + 10°)
(15) Determine the frequency at which a 50-mF capacitor has
the following capacitive reactances:
a. 342 Ω b. 684 Ω
c. 171 Ω d. 2000 Ω
(16) The voltage across a 2.5μF capacitive reactance is given.
What is the sinusoidal expression for the current?.
a. 100 sin ωt
b. 0.4 sin (ωt + 20°)
c. 8 cos (ωt + 10°)
d. 70 sin (ωt + 40°)
(17) The voltage across a 1 μF capacitor is given. What is the
sinusoidal expression for the current?
a. 30 sin 200t
b. 90 sin 377t
c. 120 sin (374t + 30°)
d. 70 cos (800t + 20°)
(18) The current through a 10 Ω capacitive reactance is given.
Write the sinusoidal expression for the voltage.
a. i = 50 sin ωt
b. i = 40 sin (ωt + 60°)
c. i = - 6 sin(ωt - 30°) d. i = 3 cos (ωt + 10°)
(19) The current through a 0.5 μF capacitor is given. What is
the sinusoidal expression for the voltage?
a. 0.20 sin 300t
b. 0.007 sin 377t
c. 0.048 cos 754t
d. 0.08 sin (1600t + 80°)
(20) For the following pairs of voltages and currents, indicate
whether the element involved is a capacitor, an inductor,
or a resistor, and the value of C, L, or R if sufficient data
are given:
a. v = 550 sin (377t + 40°)
i = 11 sin (377t - 50°)
b. v = 36 sin (754t + 80°)
i = 4 sin (754t + 170°)
c. v = 10.5 sin (ωt + 13°)
i = 1.5 sin (ωt + 13°)
(21) Repeat Problem 20 for the following pairs of voltages and
currents:
a.
v= 2000 sin ωt
i = 5 cos ωt
b. v = 80 sin(157t + 150°)
i = 2 sin(157t + 60°)
c.
v = 35 sin(ωt - 20°)
i = 7 cos(ωt - 110°)
(22) A circuit dissipates 100 W (average power) at 150 V and 2 A,
what is the power factor? Repeat if the power is 0 W; 300 W.
(23) The power factor of a circuit is 0.5 lagging. The power
delivered in watts is 500. If the input voltage is 50 sin(ωt + 10°),
find the sinusoidal expression for the input current.
(24) In the circuit shown, e = 30 sin (377t + 20°). Find :
a. the sinusoidal expression for the current?
b. the power loss in the circuit.