Physics > Alternating Current > 4.0 Circuit element in AC circuit
Alternating Current
1.0 Introduction
2.0 Alternating current and alternating voltage
2.1 Instantaneous current and voltage
2.2 Mean or average current and voltage
2.3 Root mean square current and voltage
2.4 Form factor
3.0 Some important terms
4.0 Circuit element in AC circuit
4.1 Pure resistor circuit
4.2 Pure inductor circuit
4.3 Pure capacitor circuit
4.4 Series $L-R$ circuit
4.5 Series $C-R$ circuit
4.6 Series $L-C-R$ circuit
4.7 Resonance series $L-C-R$ circuit
4.8 Quality factor
4.9 Summary
5.0 Power in AC circuit
4.5 Series $C-R$ circuit
2.2 Mean or average current and voltage
2.3 Root mean square current and voltage
2.4 Form factor
4.2 Pure inductor circuit
4.3 Pure capacitor circuit
4.4 Series $L-R$ circuit
4.5 Series $C-R$ circuit
4.6 Series $L-C-R$ circuit
4.7 Resonance series $L-C-R$ circuit
4.8 Quality factor
4.9 Summary
Consider a capacitor of capacitance $C$ and a resistor of resistance $R$ is connected to an AC supply as shown in the figure.
For phasor diagram we can write,
Phasor diagram of resistor $+$ Phasor diagram of capacitor $=$ Phasor diagram of circuit
So, voltage $V$ can be written as,
$$V = {V_R} + {V_C}$$$$V = iR + \left( {i{X_C}} \right)\left( { - \hat j} \right)$$$$V = i\left( {R - \hat j\,{X_C}} \right)$$$$V = i\left( {R - \frac{{\widehat j}}{{\omega C}}} \right)$$$$V = iZ$$
where, $$Z = R - \widehat j\left( {\frac{1}{{\omega C}}} \right)$$
The modulus of impedance can be written as,
$$\left| Z \right| = \sqrt {{R^2} + {{\left( {\frac{1}{{\omega C}}} \right)}^2}} $$
The angle by which the potential difference leads the current is, $$\tan \phi = \left( {\frac{{{V_C}}}{{{V_R}}}} \right)$$$$\tan \phi = \left( {\frac{{{X_C}}}{R}} \right)$$$$\tan \phi = \left( {\frac{1}{{\omega CR}}} \right)$$or $$\phi = {\tan ^{ - 1}}\left( {\frac{1}{{\omega CR}}} \right)$$
