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Volt_Current_Div v4

# Volt_Current_Div v4 - Founda'ons of Circuit Analysis: ...

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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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