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Voltage and current for a circuit with t...

Voltage and current for a circuit with two elements in series are expressed as
`V(t)=170sin(6280t+pi/3)volt`
`i(t)=8.5sin(6280t+pi/2)amp`
(a) Plot the two waveforms.
(b) Determine the frequency in Hz.
(c) Determine the power factor starting its nature.
(d) What are the values of the elements?

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
(b)`f=omega/(2pi)=6280/(2xx3.14)=1000Hz`
(c) `phi=pi/2-pi/3=pi/6 or 30^@`
power factor `=cosphi=cos30^@`
`(sqrt(3))/(2)`
From the given functions of `V ` and `i` we can see the curent function leads the voltage function.
(d) `z=170/8.5=20Omega` ....(i)
`cosphi=sqrt3/2=R/Z=R/20`
`:. R=10sqrt3Omega=17.32Omega`
`X_C=sqrt(Z^2-R^2)`
`=10Omega`
`C=1/(omegaX_C)=1/(6280xx10)F`
`=15.92xx10^-6F`.
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