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Equivalent Resistance
Equivalent Resistance
• A single resistor or a group of resistors
can have one or more equivalent
resistance circuits
Prepared by Engr. JP Timola
Reference: Electric Circuit
Analysis by Johnny Tan
Equivalent Resistance
Current in a resistor
• Must be able to perform the function
of the original resistor or group of
resistor
• Can be in either direction
• Must not affect the currents and
voltages in other parts of the circuit
• Can describe the polarity of potential
difference across the device
Potential Difference
• Potential difference across terminals a
and b is designated as Vab
• Vabb stands for Va-V
Vb
• Does not affect resistance
Interconnections
• Node is a point of connection of 2 or
more devices
• Major node for 3 or more connected
• Vab is positive if Va >Vb called “voltage
drop”
• “Voltage rise” if otherwise
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Interconnections
• Electric network is the interconnection
of 2 or more devices
• Electric circuit is formed if the network
contains at least one closed path
Resistors in Series
• RT = R1+ R2 + R3…
• I T = I 1 = I 2 = I 3…
• VT = V1 + V2 + V3…
Resistors in Parallel
IT = I1 + I2 + I3…
VT = V1 = V2 =V3 …
1
1
1
1
 
 ...
RT R1 R2 R3
Resistors in Series
• Resistors are in series if they are
connected end-to-end
• Each carry the same current
• No
N more than
th
2 resistor
i t connected
t d to
t
same node
Resistors in Parallel
• In parallel if constant potential
difference is applied across them
• End terminals are connected to same
node or conductor
Two Resistors in Parallel
RR
1
 1 2
RT R1  R2
I 2  IT
I1  IT
R2
R1  R2
R1
R1  R2
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PROBLEM 1
• Determine the equivalent resistance
with respect to terminals a and b
PROBLEM 3
• Determine the equivalent resistance
with respect to terminals a and b
PROBLEM 5
• Determine the equivalent resistance
with respect to terminals a and b
PROBLEM 2
• Determine the equivalent resistance
with respect to terminals a and b
PROBLEM 4
• Determine the equivalent resistance
with respect to terminals a and b
PROBLEM 6
• Determine the unknown currents
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PROBLEM 7
EQUIVALENT THREE TERMINAL
NETWORKS
• Determine the unknown currents
• when electric circuit contain networks
neither in series or in parallel, we can
replace some parts of the circuit by
their three-terminal equivalents
EQUIVALENT THREE TERMINAL
NETWORKS
• Any passive three-terminal network
may be reduced to any one of the
networks:
• Delta (∆) or Pi (π)
Wye(Y) or tee (T)
PROBLEM
• Determine the equivalent resistance
between a and b
DELTA NETWORK AND ITS WYE
EQUIVALENT
R12 
R1 R2  R2 R3  R3 R1
R3
R1 
R12 R31
R12  R23  R31
R23 
R1 R2  R2 R3  R3 R1
R1
R2 
R12 R23
R12  R23  R31
R31 
R1 R2  R2 R3  R3 R1
R2
R3 
R31 R23
R12  R23  R31
PROBLEM
• Determine the currents indicated
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PROBLEM
• Determine the equivalent resistance
between a and i
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