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AC Circuits

# Series RL Circuit

On the basis of the discussion of impedance and the Ohm's-law equation, series AC circuits can now be investigated.

Consider the circuit of figure above. The impedance * Z* of the
circuit is the phasor sum of the inductive reactance and the resistance,
since these components are in series:

Applying Ohm's law,

Converting 900 + *j*650 to polar form,

Since the circuit of figure above contains inductive reactance, it is to
be expected that the current will lag the voltage. However, since the circuit
is not pure inductance, the current will not lag by a full 90°. The current
phasor was calculated and found to be lagging by 35.8°. The phase
relationship between applied voltage * V* and current

*is shown on the complex plane of figure below.*

**I**In a series circuit, the sum of the phasors of the voltage drops must equal the applied voltage phasor.

For the series RL circuit,

This is simply the algebraic transformation of the Ohm's-law equation.
The value of **V**_{R} and
**V**_{L} may now be calculated:

Plotting **V**_{R} and **V**_{L} on the
complex plane of figure above shows that the voltage across the resistance is
in phase with the current. The voltage across the inductance leads the
current by 90°.

The phasor sum of **V**_{R} and **V**_{L}
is given by