HOW RC CIRCUIT GIVE A PHASE SHIFT TO INPUT

 

RC Hi pass circuit
Let V_in =V_m sin ω t    ---(1)

Then the impedance of the circuit can be written as

Z = R + 1/j ωc = R-j Xc           ---(2)

 

Where Xc =1/(2πfc) = |Z| Ŀ-Ф    ---(3)

Eqn (2) is in rectangular form so we can find the magnitude by the general eqn

|Z| = √(A²+B²) i.e. √[R²+(-Xc)²]

 

The same way angle

Ф =tan^-1 ( ^B/_A) = tan^-1 ( ^-Xc/_R) = tan^-1 (^-1/_ωCR)   ---(4)

 

The voltage at the output is proportional to current flowing through the resistor

I=V/R

where Vm/√2 is rms value of voltage

 

I =|I| Ŀ+Ф⁰ A

The positive angle +Ф⁰ indicates that the current leads the applied voltage by angle Ф

V=IR

As mentioned earlier Vo is the o/p voltage drop across the resistor and so is in phase with I the out put voltage will lead the input voltage by angle Ф

 

From the eqn no (4) we can find out the angle b/w i/p and o/p the phase angle offered by the RC circuit is in b/w 0⁰ and 90⁰, the 90⁰ phase shift is achieved only if the resistance, capacitance or angular frequency tends to zero. Decrees in capacitance will result