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
4.1 Pure resistor 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
The circuit containing only a pure resistor in the AC circuit is known as pure resistance circuit.
Consider a pure resistor of resistance $R$ is connected to an alternating current as shown in the figure.
Let current $i$ flows in the circuit, when the AC power supply is $V$ at any time $t$.
So, from Kirchoff's loop law we can write, $$V - iR = 0$$$${V_0}\sin \omega t = iR$$$$i = \frac{{{V_0}\sin \omega t}}{R}\quad ...(i)$$or$$i = {i_0}\sin \omega t$$
where,
${i_0} = \frac{{{V_0}}}{R}\ :$ Current amplitude
${V_0}:$ Voltage amplitude
$R:$ Resistance
Equation $(i)$ can also be written as, $$i = \frac{{{V_0}}}{Z}\sin \omega t$$
For pure resistor circuit impedance $(Z)$ is equal to the resistance of the circuit.
Mathematically impedance for pure resistor circuit is given by,
$$Z = R$$
In pure resistor circuit, alternating voltage is in phase with the alternating current.
So, we can draw the phasor diagram for the AC voltage $V = {V_0}\sin \omega t$ and alternating current $i = {i_0}\sin \omega t$ as,
If we are intrested only in phase relationship then the phasor diagram may also be represented as,
