Resistance-Inductance (R-L) series circuit is the case most generally met with in practice; nearly all circuits contain both resistance and inductance.

Consider an ac circuit consisting of resistance of R ohms and inductance of L henrys connected in series, as shown in Fig. 4.5 (a).

Let the supply frequency be f and current flowing through the circuit be of I amperes (rms value).

Now voltage drop across resistance, VR = I R in phase with the current.

Voltage drop across inductance, VL = I XL = I ω L leading I by π/2 radians, as shown in Fig 4.5 (c).

The applied voltage, being equal to the phasor sum of VR and VL, will be given by the diagonal of the parallelogram.

Quantity √R2 + XL2 is known as impedance, denoted by Z and is expressed in ohms.

From phasor diagram it is also evident that the current lags behind the applied voltage V by angle which is given by:

Since XL and R are known, the value of phase angle ɸ can be computed.

If the applied voltage v = Vmax sin ω t, then expression for the circuit current will be:

#### Impedance Triangle:

If a triangle ABC is drawn so that AB = VR/I = R, BC = VL/I = XL and AC = V/I = Z, it is a triangle similar to that produced by the voltage triangle. Such a triangle is called an impedance triangle, which is most useful in letting one see at a glance how R, X, and Z are related to each other. The angle between Z and R sides of the impedance triangle is known as phase angle of the circuit and cos of this angle is known as power factor of the circuit.

Power factor = Cos ɸ = R/Z

#### Power in Resistance—Inductance (R-L) Circuit:

Where V and I are the rms values of voltage and current and ɸ is the phase angle between applied voltage V and circuit current I.

Alternatively power consumed by the circuit: