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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 vL0 and vR0 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 90o; VL0 therefore leads v0 by 90o, as can be seen from Figure 2.

The resultant voltage is given by

v02= vR02 + vL02 = i02R2 + i02XL2

The current in the circuit is therefore: io =vo/[XL2 + R2]1/2
and the impedance (Z) is:

Z = [XL2 + R2]1/2 = [w2L2 + R2]1/2

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

tan f = vL0/vR0 = wL/R
© Keith Gibbs 2011