Question

PHY232: AC practice problems 1. The inductance and capacitance of the oscillatory circuit o f a radio station are 10 mH and 0.25 ?F wavelength of the transmitted waves (neglect resistance effect). respectively. Find the frequency and f A transformer with primary and seconda use velocity of light c-3 x10°m/s9.42 x10 m 2. ry voltage of 2000 volt and 200 volt takes a current 0.5 amp from the mains. Calculate the resistance connected across the secondary Primary power = Secondary power at the end o the circuit they are 3. A 12 ohm resistanc e and an inductance o 0.05 ? henry are connected in series connected to a 130 volt alternating voltage offrequency 50 Hz, Calculate the impedance, An electric motor has an effective resistance of 32.0 ? and an inductive reactance of 450 ? when working the alternating source is 420 V. Calculate the current amplitude. 4. under load. The voltage amplitude across alterr -m-= 7.61 A ; Remember Current amplitude lo-V2 1mns) if you write the ber Current amplitude 10V2 Irms, If you write the equation in ,ms 5. An ac generator with emf amplitude Vms 220 V and operating at frequency 400Hz causes oscillations in F. Find (a) the capacitive reactance Xc terms of amplitude you will get same answer, since V,- 150mH, and C-24.0 series RLC circuit having R 220 ?, L b) the impedance Z, and (c) the current amplitude I. A second capacitor of the same capacitance is then connected in series with the other components. Determine whether the values of (d) Xc, (e) Z, and 0I increase, decrease, or remain the same.

Please solve Q1.Thanks

Answer 1

1)

Given

$L=10\,mH=10\times 10^{-3}\,H$

and

$C=0.25\,\mu F=0.25\times 10^{-6}F$

The angular frequency of the wave is given by

$\omega=2\pi f=\frac{1}{\sqrt{LC}}$

Hence, the frequency of the wave emitted from the radio station is given by

$f=\frac{1}{2\pi\sqrt{LC}}=\frac{1}{2\pi\sqrt{10\times 10^{-3}\times 0.25\times 10^{-6}}}=3183.1\,Hz$

the wavelength is

$\lambda =c/f=\frac{3\times 10^8}{3183.1}=94247.8\,m=9.42\times 10^4\,m$