9. Impedance and Phase Angle
Impedance
The impedance of a circuit is the total effective resistance to the flow of current by a combination of the elements of the circuit.
Symbol: Z
Units: Ω
The total voltage across all 3 elements (resistors, capacitors and inductors) is written
VRLC
To find this total voltage, we cannot just add the voltages VR, VL and VC.
Because VL and VC are considered to be imaginary quantities, we have:
Impedance VRLC = IZ
So Z = R + j(XL - XC)
Now, the magnitude (size, or absolute value) of Z is given by:
Phase angle
Angle θ represents the phase angle between the current and the voltage.
Compare this to the Phase Angle that we met earlier in Graphs of y = a sin(bx + c).
Example 1:
A circuit has a resistance of 5 Ω in series with a reactance across an inductor of 3 Ω. Represent the impedance by a complex number, in polar form.
Example 2 (a):
A particular ac circuit has a resistor of 4Ω, a reactance across an inductor of 8 Ω and a reactance across a capacitor of 11 Ω. Express the impedance of the circuit as a complex number in polar form.
Flash Interactive
Here is a Flash example to play with. Play with the sliders to see the effect of each component. Also, you can enter your own values.
Activities for this Flash Interactive
- First, just play with the sliders and observe the effects on the values of XL - XC and Z. Also, consider the graphs of voltage and current in the bottom right corner.
- Set each of the sliders to 0. Why does the graph of current disappear?
- On paper, calculate Z and θ if R = 60 Ω, XL = 50 Ω and XC = 90 Ω.
- Now click where it says "Own values" and enter the values that you found in Activity 3 above (R = 60 Ω, XL = 50 Ω and XC = 90 Ω) to check your answer. Observe the amount of lag or lead in the bottom right corner.
- What have you learned from playing with this Flash movie?
Click where it says "Start"
Example 2(b):
In example 2 (a) above, suppose we have a current of 10 A in the circuit. Find the magnitude of the voltage across
i) the resistor (VR)
ii) the inductor (VL)
iii) the capacitor (VC)
iv) the combination (VRLC)
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