An AC circuit has a voltage of 140coswt V There is also a 39

An AC circuit has a voltage of 14.0cos(wt) V. There is also a 390. Ohm resistor and a 1.60 nF capacitor in the circuit. What is the value of V_R and V_C if the emf frequency is 1.30 kHz? V_R = 14.0 V and V_C = 0.668V V_R = 0.668 Vand V_C = 14.0 V V_R = 14.0 V and V_C = 0.0714 V V_R = 0.0714 V and V_C = 14.3 V Question 2 You v/ant a resonance frequency of 1.27 times 10^3 Hz and already have a circuit with a 115 Ohm resistor and a 23.0 mH inductor. What capacitor should be added in series to get the correct frequency? 1.89 times 10^-6 F 3.67 times 10^5 F 6.83 times 10^-7 F 3.25 times 10^-6 F Question 3 A toaster oven dissipates 1.74 times 10^3 W of power when connected to a power line that has a voltage rating of 173 V and a frequency of 61.0 Hz. What is the resistance of the toaster oven? 0.0703 Ohm 3.01 times 10^5 Ohm 10.1 Ohm 17.2 Ohm

Solution

1.

Answer is V_R=0.0714 V ,V_C =14 V

Capacitive reactance

X_C=1/2pifC =1/2pi*(1.3*10³)(1.6*10^-9) =76517 ohms

Impedance

Z=sqrt[R²+X_C²] =sqrt[390²+76517²]=76517.8 ohms

Total Current

I=V/Z =14/76517.8=1.83*10^-4 A

Voltage across resistance

V_R=IR =390*(1.83*10^-4)=0.0714 Volts

Voltage across capacitor

V_C=IX_C =(1.83*10^-4)*76517 =14 Volts

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2.

Resonant frequency

f=1/2pisqrt[LC]

=>C=1/4pi²f²L =1/4pi²*(1.27*10³)²(23*10^-3)

C=6.83*10^-6 F

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3.

Resistance of the toaster is

R=V²/P =173²/(1.74*10³)

R=17.2 ohms