LCR circuit AC circuit containing Inductance, Capacitance and resistance

 

AC circuit containing

Inductance, Capacitance

And resistance

(LCR-circuit)

 

1) In a circuit an AC voltage is applied, containing Inductance capacitance, & resistance.

2) As they are connected to the AC source, Suppose I is the current flowing through it, then

3) The maximum potential across the resistance, inductor and capacitor is   I₀R,   I₀X_L  &   I₀X_C  respectively.   

1) Let the current  I₀  is represent along the X-axis that is along OX.

2) As for capacitance the potential  V_C = I₀X_C  is behind the current by  so it is along the negative of Y-Axis.

3) And for inductor the voltage V_L = I₀X_L  is ahead of  so it is along the positive of Y-Axis. 

4) As V_L   &   V_C  are two in opposite direction. 

Suppose V_L > V_C  

 

5) Then V_L - V_C   is also along the positive Y-Axis. 

6) Now the resultant of V_L - V_C   and V_R  is shown in the diagram V_result

7) V_result making an angle  with the V_R then from trigonometry we find that

 

Now

Here z is like a resistance in the circuit called the impedance of the circuit.

Now we have

Case 1: when

XL = XC

Then

So,

In this scenario the current and the voltage are in same phase and the circuit is called non-inductive.

Case 2: if

XC > XL

Then

is negative and the circuit is predominantly capacitive.

Case 3: when

XL > XC

Then

is positive and the circuit is predominantly inductive.