The Bridge Rectifier

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{5}A_{51} Base Sequence = 12735 String Sequence = 12735 - 5 - 51**

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The Bridge Rectifier

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The half-wave rectifier converts only the positive half-cycle of an AC input signal. So, the negative half-cycle is unused. The bridge rectifier is a full-wave rectifier that coverts both cycles of the AC signal.

(a) Circuit 121.9 (a) is a *bridge rectifier*. Which diodes are conducting during the positive AC cycle and which diodes are conducting during the negative AC cycle?

The *box* of 121.9(b) and its AC input and DC output represents an Integrated Circuit (IC) Rectifier. An integrated circuit is a collection of electronic circuits on a silicon chip.

(b) Why are the resistor and capacitor added in the circuit of figure 121.9(b)?

(c) Suppose the bridge rectifier of circuit 121.9(a) is used to provide a 50 v, 5 A DC supply. Determine the resistance of the load that will draw exactly 5 A and the rms source voltage that realized the desired DC voltage. Assume an ideal diode.

**The strings**:
S_{7}P_{5}A_{51} (Physical Change).
**The math**:

Pj Problem of Interest is of type *change* (physical change). The *bridge rectifier* is a *change* device. It *changes* each cycle of an AC signal to a DC signal.

(a) D1 an D3 will conduct during the positive AC half-cycle. D2 and D4 will conduct during the negative AC cycle.

(b) The resistor, capacitor (RC) act as a low pass filter. The role of the filter is to remove most of the remaining AC component in the DC output. Rectifier circuits tend to pulsate about a mean average. The filter removes most of the fluntuations.

(c) Load resistance, R_{L} = 50/5 = 10 ω

load voltage v_{L} = R_{L} (i_{L}) = (R_{L} /T)∫_{0} ^{T} i(t) dt

Where T = 2π/ω

So, v_{L} = (R_{L} /T)∫_{0} ^{T/2} (v_{peak}/R_{L})sinωt dt

So, v_{L} = 2v_{peak}/π = 2√2(v_{rms})/π = 50 V

So, v_{rms} = 55.5 V.

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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