2. Steady state analysis of R, L and C circuits.pptx

basic electrical circuit

1. Steady state analysis of R, L and C circuits By I V VEERANJANEYULU Dept of Electrical & Electronics Engineering Aditya Engineering College(A) Surampalem .

2. Monday, December 11, 2023 I V VEERANJANEYULU Concept of Phase angle and Phase difference A phasor diagram can be used to represent a sine wave in terms of its magnitude and angular position. The length of the arrow represents the magnitude of the sine wave and angle θ represents the angular position of the sine wave.    

3. Monday, December 11, 2023 I V VEERANJANEYULU or or

4. Monday, December 11, 2023 I V VEERANJANEYULU Draw the phasor diagram to represent the two sine waves shown in fig.

5. Monday, December 11, 2023 I V VEERANJANEYULU Phasor Relationships for Circuit Elements Resistor If the current through a resistor R is i (t) = I m cos ( ω t+ Φ ), then voltage across it is given by Ohm’s law as v(t) = i (t)R = RI m cos ( ω t+ Φ ) The phasor form of this voltage is V = RI m ∠ Φ But the phasor representation of the current is I = I m ∠ Φ. Hence, V = R I Phasor diagram for the resistor. In case of resistor, Voltage wave form follows current wave form. Voltage phasor and current phasor are in phase. The impedance Z of a circuit is the ratio of the phasor voltage V to the phasor current I , measured in ohms (Ω).

6. Monday, December 11, 2023 I V VEERANJANEYULU Inductor In case of inductor, current waveform lags voltage waveform by 90 . Voltage phasor and current phasor are out of phase by 90 , voltage phasor leads current phasor by 90 or current phasor lags voltage phasor by 90

7. Monday, December 11, 2023 I V VEERANJANEYULU Capacitor In case of capacitor current waveform leads voltage waveform by 90 . Voltage phasor and current phasor are out of phase by 90 , voltage phasor lags current phasor by 90 or current phasor leads voltage phasor by 90 .

8. Monday, December 11, 2023 I V VEERANJANEYULU The admittance Y is the reciprocal of impedance, measured in siemens (S) Frequency (ω) is 0 for dc. Frequency (ω) is ∞ at high frequencies Z = jωL = 0 Z = jωL = ∞

9. Monday, December 11, 2023 I V VEERANJANEYULU Steady state analysis of RL series circuit

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12. Monday, December 11, 2023 I V VEERANJANEYULU Steady state analysis of RC series circuit

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15. Monday, December 11, 2023 I V VEERANJANEYULU The impedance may be expressed in rectangular form as Z = R ± jX where Re[Z] is the resistance R and Im [Z ]is the reactance X. The reactance X may be positive or negative . The impedance is inductive when X is positive or capacitive when X is negative. Thus, impedance Z = R + jX is said to be inductive or lagging since current lags voltage, while impedance Z = R - jX is capacitive or leading because current leads voltage. The impedance, resistance, and reactance are all measured in ohms. Admittance, conductance, and susceptance are all expressed in the unit of Siemens (or mhos).

16. Monday, December 11, 2023 I V VEERANJANEYULU Steady state analysis of RLC series circuit

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