Answer to Question #294122 in Electrical Engineering for her

Question

a.      At what point in an RLC circuit does resonance occur?       [3marks]

b.     The resonant frequency of a series RLC circuit is 2380kHz when the current is 560 PA and the voltage across it is 240mV. If the value of the inductance in the circuit is 60gH, find the resistance and the capacitance.

[6 marks]

c.      A resistor of 150, an inductor of 0.0318H and a 150uF capacitor are connected in series to a 240V sinusoidal supply at 50Hz. Calculate:

i. The impedance of the whole circuit; [6 marks] ii. The circuit current; [3 marks] iii. The voltage across each component; [4 marks] iv. The power factor;   [3 marks]

Answer 1

a. At the resonant frequency.

b.

$$C=\dfrac1{\omega^2L}=74.5\text{ fF}.$$

c.

$$Z=\sqrt{R^2+(\omega L-\dfrac1{\omega C})^2}=150.14\Omega.\\ I=V/Z=1.6\text A.\\ \cos\phi=(\omega L-1/(\omega C))/Z=-0.075.$$