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
4.4 Series $L-R$ 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 an inductor of self inductance $L$ and a resistor of resistance $R$ is connected to AC supply as shown in the figure.
For phasor diagram we can write,
Phasor diagram of resistor $+$ Phasor diagram of inductor $=$ Phasor diagram of circuit
So, voltage $V$ can be written as,
$$V = {V_R} + {V_L}$$$$V = iR + \left( {i\omega L} \right)\widehat j$$$$V = i\left( {R + \widehat j\omega L} \right)$$$$V = iZ$$
where, $$Z = R + \widehat j\omega L$$ or $$Z = R + \widehat j\,{X_L}$$
$Z$ is known as impedance of the circuit.
The angle by which the potential differences leads the current is, $$\tan \phi = \left( {\frac{{{V_L}}}{{{V_R}}}} \right)$$$$\tan \phi = \left( {\frac{{{X_L}}}{R}} \right)$$$$\phi = {\tan ^{ - 1}}\left( {\frac{{{X_L}}}{R}} \right)$$or $$\phi = {\tan ^{ - 1}}\left( {\frac{{\omega L}}{R}} \right)$$
The modulus of impedance can be written as, $$\left| Z \right| = \sqrt {{R^2} + {{\left( {\omega L} \right)}^2}} $$
