Electrical Engineering ⇒ Topic : R-C Circuit

R-C CIRCUIT

The R-C circuit is shown in Figure (a).

                figure (a) R-C circuit.

where                                                                     ............. (1)

                                                                                         ..............  (2)

                                                                                         ................ (3)

R-C Series A.C. Circuit

Fig. (a) shows a resistance of R ohms connected in series with a capacitor of C farad.

Let                                      V = rm. s. value of applied voltage

                                            I = rm. s. value of the circuit current

                                       V_R  = IR where r'R is in phase with I

                                        V_C = IX_c where r'c lags I by 90°

Taking current as the reference phasor, the phasor diagram of the circuit can be drawn as shown in Fig. (b). The voltage drop V_R ( = IR) is in phase with current and is represented in magnitude and direction by the phasor OA. The voltage drop V_C (= IX_C) lags behind the current by 90° and is represented in magnitude and direction by the phasor AB. The applied voltage I' is the phasor sum of these two drops i . e .

                                          (a)                                                                                                               (b)

                                                                                     figure

                                                 (c)                                                                                                        (d)

                                                                                   figure 

(1) Phase angle. It is clear from the phasor diagram that circuit current I leads the applied voltage V by Φ⁰. This fact is also illustrated in the wave diagram See Fig. (c) and impedance triangle See Fig. (d) of the circuit. The value of the phase angle can be determined as under

Since current is taken as the reference phasor, negative phase angle implies that voltage lags behind the current. This is the same thing as current leads the voltage.

   If the applied voltage is v = V_m, sin ωt, then equation for the circuit current will be