Question

5. (10 points) The amplitude of the current / versus driving angular frequency wg for a driven RLC circuit is given in the figure on the right, where the vertical axis scale is set 3 by Is = 4.00 A. The inductance is 200 uH, and the emf amplitude is 8.0 V. What are (a) Cand (b) R? (100 /

Answer 1

In RLC circuit, we see that, there comes a point where on varying angular frequency, the impedance of circuit becomes minimum, giving out maximum current,

Z = (R^{​​​​​​2} + (X_{​​​​​​L} - X_{​​​​​​C})²)^0.5

This happens when X_{​​​​​​L} = X_{​​​​​​C} (inductive reactance = capacitive reactance)

When $\omega$ = 1/√(LC) , where L is inductance and C is capacitance

Now from the graph we can see that, the maximum current is achieved for 25,000 rad/s and as L is given as 200$\mu$H

Hence C = 1/(L$\omega$²)

C = 1/(200*10^-6*(25000)²) = 8$\mu$F

And at the given angular frequency, Z = R ,

Maximum current will be, E_{​​​​​​max}/Z

That is, I max given is 4A

Therefore, R = E_{​​​​​​max}/I_{​​​​​​max} = 8/4 = 2$\Omega$