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AC Circuits

Q- In an AC circuit the voltage across a resistive component is given by V(t) = 10 + 5 sin (3t). Find

(a) The voltage amplitude

(b) Root mean square voltage across the component Vrms.

Solution:

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Alternating Current Circuit

Q- Calculate the voltages V1 and V2 for the circuit shown in figure.

Solution:

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Alternating Current: Admittance

Q- For the circuit of Figure

(a) Find the total admittance in polar form.

(b) Draw the admittance diagram.

(c) Find the value of C in microfarads and L in Henries if the current in the circuit is

          I = 3 sin (377 t + 600)

Solution:

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L-R Circuit

Q- Three resistors (R1 = 120 Ohms, R2 = 330 Ohms, and R3 = 240 Ohms) and an ideal inductor (L = 1.6 mH) are connected to a battery (V = 9 V) through a switch as shown in the figure. The switch has been open for a long time before it is closed at t = 0. At what time t0, does the current through the i…

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Work Done On An Inclined Plane

Q- Gopal finds that a force F is required to push a crate of mass m up a plank of length L into a truck whose platforms is a vertical distance h above the road.

(a) How much work does Gopal do in pushing the crate up the plank?

(b) Calculate Gopal’s work input if the crate has a mass of 100 kg, …

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Magnetic Effects: Force on a loop

Q- At t=0, a rectangular coil of resistance R = 2 ohms and dimensions w = 3 cm and L = 8 cm enters a region of constant magnetic field B = 1.6 T, directed into the screen as shown. The length of the region containing the magnetic field is LB = 15 cm. The coil is observed to move at constant velocity…

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Alternating Current: Series Resonance

The cut-off frequencies of a series resonant circuit are 5400 Hz and 6000 Hz.

(a) Find the Bandwidth of the circuit.

(b) If  quality factor Q = 9.5, find the resonant frequency of the circuit.

(c) If the resistance of the circuit is 2 Ω, find the value of reactance  XL and XC at resonance…

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Electromagnetic Waves

Q- An electromagnetic wave has a frequency of 110 MHz and is traveling in a vacuum. The magnetic field is given by                                    (z, t) = (2.00 x 10-8 T) cos (k z - ω t) i.

(a) Find the wavelength and the direction of propagation of this wave.

(b) Find t…

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Sound Waves

Q- The graph bellow represents a travelling wave. Each interval on the vertical axis corresponds to 5 cm, and each interval along the horizontal axis corresponds to 0.2 s. Find the amplitude, time period, frequency and wavelength of the wave. 

Solution:

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Alternating Current: Phasor diagram

Q- Represent current wave-forms I1 = 4 cos(ωt) and I2 = 3 sin (ωt) in a phasor diagram, using sin (ωt) as the reference phasor. Now represent the resultant current waveform on the phasor diagram in the same way.  

Solution:

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Motion in a plane

Q- An object is accelerating along x axis with an acceleration of 2 m/s2 for three 3 s and attaining a velocity of 20 m/s at an angle of 300 with positive x direction.

(a) Calculate magnitude of initial velocity of the object.

(b) Find the direction of initial velocity vector.

Solution:

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AC: Inductance

Q- A pure inductance L is connected to an AC circuit and the maximum voltage across it is Vmax = 100V.

(a) If the maximum current is 7.5A at 50Hz, calculate the inductance L

(b) At what angular frequency (ω) is the maximum current 2.5A?

Solution:

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AC Circuits: Capacitive Reactance

(a) An 8.0µF capacitor is connected to the terminals of a 60Hz AC source whose rms voltage is 150V. Find the capacitive reactance and rms current in the circuit.

(b) If the frequency is doubled, calculate the new rms current.

Solution:

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Wave Optics: Interference

Q- Light of wavelength 440 nm illuminates two 35 cm glass slides. An object is placed between the ends of the slides causing an air wedge to form between the slides. 445.6 dark fringes per cm are seen on the slides. Determine the thickness of the air wedge.

Solution:

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Alternating current

Q- An alternating waveform is given by the voltage as a function of time as

             V(t) = 3 cos (2t) + 4 sin (2t)

Calculate the peak voltage, rms voltage and the phase at t = 0.

Solution:
 

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Alternating current: Impedance

Q- A series combination of R = 1000Ω, L = 500 mH and C = 150µF is connected to a sinusoidal voltage supply of frequency 50Hz. The circuit has a peak amplitude of 1A. Calculate the voltage amplitude of the supply generator.

Solution:

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Alternating current

Q- A 100 µF capacitor is connected in turn to two different sinusoidal voltages of the same amplitude V = 1.0V but different frequencies with f1 = 50Hz and f2 = 5kHz.

(a) Calculate the reactance X1 and X2

(b) By what factor is X1 greater than X2 ?

(c) Calculate the amplitudes of the associated c…

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Alternating Current

Q- A simple AC Circuit contains R=70.0 Ohm and V = Vmax sin ωt

a) If Vt = 0.250 Vmax for the first time at t = 0.0100 s, what is the angular frequency ω of the source?

b) What is the next value of t for which Vt = 0.250 Vmax?

Solution:

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Happy Independence Day

Projectile Motion

Q- An airplane with a speed of 75 m/s is climbing upward at an angle of 37.0 ° with respect to the horizontal. When the plane's altitude is 600 m, the pilot releases a package.

(a) Calculate the distance along the ground, measured from a point directly beneath the point of release, to where the p…

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