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AC circuit contains ohmic resistance , capacitor and inductive coil connected in series

From Online Sciences - April 7, 2018

Impedance

In an electric circuit containing an AC power supply together with inductive coils , capacitors and resistors , the AC current would be opposed by reactance ( inductive reactance or capacitive reactance ) in addition to the resistance of resistors and wires , The resistance and reactance together are called impedance and given the symbol ( Z ) and measured in Ohm () .

The impedance ( Z ) is the equivalent to the resistance , capacitive reactance and inductive reactance together in an AC circuit , When the impedance of RLC circuit = 300 , It means that the total opposition to the electric current in this circuit due to the resistance and the reactance of both the coil and capacitor = 300 .

AC circuit contains ohmic resistance and inductive coil connected in series ( RLcircuit )

It is almost impossible practically to construct an inductive coil with zero resistance , because any coil must have a resistance due to the wires used in its fabrication .

When electric circuit contains inductive coil , ohmic resistance and AC source connected in series , we noticed that the current passing through each of the resistance and the induction coil is the same in value and phase since they are connected in series .

But voltage in the coil ( VL) leads current ( I ) by cycle ( phase angle 90 ) in the induction coil , voltage in the resistance (VR ) is in phase with current ( I ) in ohmic resistance .

The potential difference across a coil( VL) leads the potential difference across the resistance(VR ) by a phase angle 90 , thus the total potential difference is out of phase with the current intensity ( I ) .

Total voltage can be found using the vectors from the relation :

V = VR + VL

V = I Z , VR = I R , VL = I XL

( I Z ) = I R + I XL =I ( R + XL )

Z= ( R + XL )

The phase angle can be determined between the total voltage ( V ) and the resistor voltage ( VR ) from the relation :

tan= VL / VR , tan= I XL / I R , So ,tan= XL / R

AC circuit contains ohmic resistance and capacitor connected in series ( RC-circuit )

When electric circuit contains capacitor , ohmic resistance and AC source connected in series , We notice that the current passing through each of the resistance and the capacitor is the same in value and phase since they are connected in series .

But voltage in the capacitor ( VC ) lags current ( I ) by cycle ( phase angle 90 ) in the capacitor , Voltage in the resistance ( VR ) is in phase with current ( I ) in ohmic resistance .

The potential difference across the capacitor ( VC ) lags the potential difference across the resistance( VR ) by phase angle 90 , thus the total potential difference ( V ) is out of phase with current intensity ( I ) .

Total voltage can be found using the vectors from the relation :

V = VR + VC

V = I Z ,VR = I R , VC = I XC

AC circuit contains ohmic resistance , induction coil and capacitor connected in series ( RLCcircuit )

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