Transcript Elements in Series

Resistors in Series
• Resistors connected at a single node
• Current through each resistor is the same
EGR 101 Introduction to Engineering I
1
Identify the current in each Resistor
Apply KCL at each node
iS  i1  i2  i3  i4  i5  i6  i7
a
b
c
d
e
f
EGR 101 Introduction to Engineering I
g
2
Redraw using a single current
EGR 101 Introduction to Engineering I
3
To solve for the current, write KVL
vS  iS R1  iS R2  iS R3  iS R4  is R5  iS R6  iS R7  0
vS  iS ( R1  R2  R3  R4  R5  R6  R7 )  iS Req
EGR 101 Introduction to Engineering I
4
Simplified version of the circuit
vS  iS Req
7
Req   Ri  R1  R2  R3  R4  R5  R6  R7
i 1
EGR 101 Introduction to Engineering I
5
From a “black box” point of view
• These circuits are “equivalent”
• Same current drawn from the source
EGR 101 Introduction to Engineering I
6
Summary
• Resistors in series have the same current
• The resistors can be replaced by an
“equivalent” resistance equal to the sum of
the individual resistors
• The “equivalent” resistance is larger than
the largest of the individual resistors
EGR 101 Introduction to Engineering I
7