AC Through Resistance and Capacitance

AC Through Resistance and Capacitance

AC Through Resistance and Capacitance

The circuit for AC Through Resistance and Capacitance is shown in Figure (A) . Here VR = IR = drop across R in phase with I.  VC = IXC = drop across capacitor –lagging I by π/2

As capacitive reactance XC is taken negative, VC is shown along negative direction of Y-axis in the voltage triangle [Figure (B)]

AC Through Resistance and Capacitance
Figure A
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AC Through Resistance and Capacitance
Figure B

The denominator is called the impedance of the circuit.  http://engg.mcqsduniya.in/wp-content/uploads/2021/03/AC-Through-Resistance-and-Capacitance-4.jpg 

AC Through Resistance and Capacitance
Figure C

Impedance triangle is shown in Figure (C)
From Figure (B) it is found that I leads V by angle φ such that tan φ = − XC/R

Figure D

Hence, it means that if the equation of the applied alternating voltage is v = Vm sin ωt, the equation of the resultant current in the R-C circuit is i = Im sin (ωt + φ) so that current leads the applied voltage by an angle φ. This fact is shown graphically in Figure (D).

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