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Example
What is the voltage (Vrms) drop across the capacitor in a series RC circuit where the applied
voltage is 10 Vrms and resistor voltage drop is 6 Vrms.?
E  E 2R  E C2
10 V  62  E C2
E C2  100  36  64 V 2
E C2  8 Vrms
IMPEDANCE
Impedance is the total opposition to current flow in any circuit although the term is often
reserved for the apparent resistance in an AC circuit. In short, impedance is generalized
resistance of a circuit including contributions from resistors, capacitors, inductors, etc. In a
circuit consisting of a resistor and a capacitor, the total opposition is the sum of the capacitive
reactance and the DC resistance. Both the reactance and the resistance impede current flow. For
an RC circuit, the impedance is the vector sum of the capacitive reactance and resistance.
The impedance of an AC circuit is expressed in ohms and is designated by the letter Z. We can
define the impedance in terms of Ohm's law just as we defined the total resistance of a DC
circuit.
E  I Z
This expression can be rearranged using basic algebra to obtain the expressions for voltage and
current in terms of the circuit impedance:
In the previous section, we saw that because of the phase shift caused by the capacitor in a series
RC circuit, the voltage drops across the capacitor and resistor could not be added directly to
obtain the applied voltage. Instead, a vector sum had to be taken in order to obtain the correct
value. Since the current through a series circuit is the same in all elements, we can say that the
voltage drops across the circuit components are directly proportional to their resistance or
reactance. For that reason, we can draw a diagram
exactly like the voltage vector diagram described
earlier, to obtain the total impedance of the circuit,
as shown on the left. Here the current vector is
again used as the reference. The resistance vector is
coincident with the current vector since the resistive
voltage drop is in phase with the current. In this
case, the length of the vector is proportional to the
resistance. Another vector representing the
magnitude of the capacitive reactance, XC, is drawn
90° out of phase with the resistance vector to take
into account the 90° phase shift produced by the
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