The LR (inductance-resistance) circuit

The circuit in Figure 1 contains both inductance and resistance. As with the capacitance-resistance circuit, the current through it depends on the value of both the components and the frequency of the supply voltage.

Let the supply voltage be v₀ and the voltages across the inductor and the resistor be v_L0 and v_R0 respectively. Now we know that for a resistor the current and voltage are in phase, while for an inductor the current leads the voltage by 90^o; V_L0 therefore leads v₀ by 90^o, as can be seen from Figure 2.

The resultant voltage is given by


v₀²= v_R0² + v_L0² = i₀²R² + i₀²X_L²

The current in the circuit is therefore: i_o =v_o/[X_L² + R²]^1/2
and the impedance (Z) is:



The phase angle for this circuit (φ) (see Figure 3) is given by