what if the frequency is now increased to/ = 70 Hz, and we want to keep the impe

Question

what if the frequency is now increased to/ = 70 Hz, and we want to keep the impedance unchanged? (A) What new resistance should we use to achieve this goal? R= Follow the example closely. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. (B) What is the phase angle (in degrees) between the current and the voltage now? (C) Find the maximum voltages across each element.

Explanation / Answer

A) impedance, Z = R + j(XL - Xc)

      = R + j( (2pi f L) - (1 / (2pifC))

   = 410 + j (527.8 - 716.91) = 410 - j189.11

|Z| = sqrt(410^2 + 189.11^2) = 451.51 ohm

now XL = 2 xpi x 70 x 1.40 = 615ohm

Xc = 1 / (2 pi x 70 x 3.7 x 10^-6) = 615 ohm

Z = R + j (615 - 615) = R

hence R = 451.51 ohm

B) phase angle, @ = tan^-1( (XL- Xc) / R) = 0

C) I = Vmax / |Z| = 150 / 451.51 = 0.332 A

Vr = I R = 150 V

VL = 615 x 0.322 = 204.31 V

Vc = 204.31 V

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