Question #108875
1.

A 400 mH coil of negligible resistance is connected to an AC circuit in which an effective current of 6 mA is flowing. Find out the voltage across the coil if the frequency is 1000 Hz.

2.

A capacitor of capacitance 102/π µF is connected across a 220 V, 50 Hz A.C. mains. Calculate the capacitive reactance, RMS value of current and write down the equations of voltage and current.

3.

Find the impedance of a series RLC circuit if the inductive reactance, capacitive reactance and resistance are 184 Ω, 144 Ω and 30 Ω respectively. Also calculate the phase angle between voltage and current.
1
Expert's answer
2020-04-10T13:40:03-0400

1) The voltage can be found by Ohm's law:


V=IXL=IωL=I2πfL=15 V.V=IX_L=I\omega L=I\cdot2\pi fL=15\text{ V}.

2) The capacitive reactance is


XC=12πfC=98 Ω.X_C=\frac{1}{2\pi fC}=98\space\Omega.

RMS value of current:


I=VXC=2.2 A.I=\frac{V}{X_C}=2.2\text{ A}.


3) The impedance of a series RLC circuit is


Z=(XLXC)2+R2=50 Ω.Z=\sqrt{(X_L-X_C)^2+R^2}=50\space\Omega.

The phase angle between voltage and current equals


ϕ=atanXLXCR=53.\phi=\text{atan}\frac{X_L-X_C}{R}=53^\circ.


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