IAN LANG ELECTRONICS

# Crib sheet for Impedance

### Calculating Capacitive Impedance

When we calculated Xc before we used the formula Xc=1/(2 f C) . In our example we are given no example frequencies. Let’s have two of them so we can compare the effects. For the first, we shall have 50 Hz, and for emphasis the second can be 10Hz.
As before, we need to get our units straight. Let C be in Farads:
200/1000000 = 0.002F,
let R be in ohms:
2 x 1000000 = 2,000,000 ohm

So, let's do Xc at 50 Hz:

multiply that answer by 2 = 0.0628

now put that as a reciprocal 1 / 00628 = 15.9 ohms of capacitive reactance (Xc).

At 10 Hz:

10 X 0.0002 = 0.002

multiply that by 2 = 0.01256

and now the reciprocal 1 / 0.01256 = 79.6 ohms of capacitive reactance (Xc).

This illustrates an important point: Xc goes down as frequency goes up.
Our impedance at 50 Hz then is:

Z = 2,000,000 + 15.91 and squaring everything on the right hand side:

Z = 4,000,000,000,000 + 253.13 and adding them up:

Z = 4000,000,000,253.1281 if that’s Z2 then finding the square root gives us Z:

Z = 2,000,000.000063284 ohms of total impedance.

and thus the circuit contains hardly any reactance at all in comparison. The power factor of such a circuit would be as close to 1 as to make scant difference
If we were to work the 10Hz frequency in the same way we’d get an answer of 2,000,000.001583 ohms which is still almost entirely resistive. This is because the resistor is such a big value. Nevertheless an important point has been illustrated : unlike resistance impedance is dependent upon the frequency of the supply. And for capacitors, as frequency goes up, reactance goes down. As reactance goes down, so does impedance.

The above is given as question 5 in BTEC assesment 2. The below is question 10, which concerns itself with doing the same thing for inductors.

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