**Question 6: Explain the term impedance of an AC circuit. Find expression for the impedance of the RLC series circuit.**

ANSWER

#### Impedance

An AC circuit may consist of a resistor R, a capacitor C and inductor L in combination. The combined opposition offered to the flow of AC current by these elements is called impedance. It is defined as,

“*The ratio of the rms value of the applied voltage to the rms value of the resulting current.”* Mathematically,

Z being the impedance of the AC circuit.

#### Unit of impedance

Unit of impedance is ohm, denoted by Ω. . Impe*dance of a circuit is said to be one ohm if a current of one rms Ampere flows in the circuit when the voltage across its terminals is one rms volts.*

#### Impedance of the RLC series circuit

Consider resistance R, inductance L and capacitance C connected in series in an AC circuit. We note that;

- Potential difference V
_{R}across the resistance R is in phase with the current and given by -
Voltage V

_{L}across the inductance L leads the current by π/2 rads. -
Voltage drop across C is lagging behind the current by π/2 rad.

Therefore, V_{L} and V_{C} are out of phase by π rads. This is shown in the vector diagram.

#### Impedance calculation

The applied voltage is equal to the vector sum of V_{R}, V_{L} and V_{C}. Let V_{L}>V_{C}, then their sum is V_{L} – V_{C} which is directed in the upward direction along V_{L. }The net applied voltage is, therefore, somewhere in the first quadrant between V_{L} and V_{R} as shown in the figure.

The magnitude of the applied voltage is

Now we know that V_{R} = IR, V_{L} = IX_{L} and V_{C} = IX_{C}. Therefore, the above equation can be written as

Total impedance of the circuit is

For this particular arrangement (X_{L}>X_{C}), the voltage is leading the current by an angle φ, called the phase angle. However, when X_{C}>X_{L}, the voltage is lagging behind the current. Both the situations are depicted in the diagram to the right. These are called impedance triangles.

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