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Unformatted text preview: Founda'ons of Circuit Analysis: Voltage and Current Dividers DePiero EE 201 Learning Objec'ves • Simplify series and parallel elements to form equivalent circuits • Apply voltage and current divider laws • Notes: – Ad hoc method. Expedi'ous in some cases. – Qualita've underpinning (vs Mesh Analysis which is more systema'c and strictly quan'ta've). Simplify Circuits Using Equivalent Resistors • Resistors in series add to form equivalent: Req = R1 + R2 + ... + Rn • Resistors in parallel may also be combined: €
Req = 1
11
1
+
+ ... +
R1 R2
Rn • Note: Req < Min{Ri} • Helpful when ﬁnding e€
quivalent circuits… Voltage Dividers Yield Frac'on Of Voltage Source – For R in Series • Find V2, across R2
– Find I:
– Use I to find V2 Vs
Vs
=
Req R1 + R2
Vs
V2 = I R2 =
R2
R1 + R2
I= € • Rearrange to yield voltage divider:
€
V2 = Vs R2
R1 + R2 • And, with additional resistors in series:
€ € V2 = Vs R2
R1 + R2 + ... + Rn Current Dividers Yield Frac'on Of Current Source For R in Parallel • Find I2 thru R2:
– Find V: V = Is Req = Is – Use V to find I2:
€ I2 = 1
1
1
+
R1 R2 V
1
1
= Is
1
1 R2
R2
+
R1 R2 • Rearrange to yield current divider:
€
I2 = Is 1
R2
1
1
+
R1 R2 • With more parallel resistors: I2 = Is €
I2 = Is € 1
R2
1
1
1
+
+ ... +
R1 R2
Rn
G2
G1 + G2 + ... + Gn ...
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This note was uploaded on 10/24/2011 for the course EE 251 taught by Professor Arakaki during the Spring '08 term at Cal Poly.
 Spring '08
 ARAKAKI
 Volt

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