Please help! In a purely inductive circuit of 20.7 mH, the frequency is 38.1 Hz

Question

Please help!

In a purely inductive circuit of 20.7 mH, the frequency is 38.1 Hz and the maximum voltage is 193 V. Find the rms current in the circuit. Answer in units of A Repeat for a frequency of 8040 Hz. Answer in units of A A certain capacitor in a circuit has a capacitive reactance of 33.1 12 when the frequency is 59.4 Hz. What capacitive reactance does the capacitor have at a frequency of 14300 Hz? Answer in units of 12 A 75 il resistor is connected in series with a 54 mH inductor and a 0.2 muF capacitor. The applied voltage has the form S = 190 V sin(27r ft), where the frequency is f = 830 cycles fs. Find the rms current. Answer in units of A Find the rms voltage across R. Answer in units of V Find the rms voltage across L. Answer in units of V Find the rms voltage across C. Answer in units of V

Explanation / Answer

001:

XL = 2pifL = 2*3.14* 38.1* 0.0207 = 4.95 ohms

current i = V/XL = 193*1.414/4.95 = 55.131 Amps

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XL = 2pifL = 2*3.14* 8040* 0.0207 = 1045.16 ohms

current i = V/XL = 193*1.414/1045.16 = 0.2611Amps

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3:XC = 1/(2pifC)

C = 1/(2*3.14* 59.4*33.1)

C = 81 uF

so XC = 1/(2*3.14* 8040*81uF)

Xc = 0.244 ohms

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04:XL = 2pifL = 2*3.14* 830* 0.054 =281.469 ohms

Xc = 1/( 2*3.14* 830* 0.2uF)

Xc = 959.25 ohms

Z^2 = 75^2 +(959.25-281.469)^2

Z = 681.91 ohms

current i = 190/681.91 = 0.278 Amps

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005: Vrms = 190/1.414 = 134.37 volts

Vrms across R = iR = 0.278 *75/1.414 =14.75 volts

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VL = iXL = 0.278 *281.469/1.414= 55.33 volts

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0.06:

Vrms C = 0.278 *959.25/1.414= 188.59 volts

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